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LED-Lidar Echo Denoising Based on Adaptive PSO-VMD

LED-Lidar Echo Denoising Based on Adaptive PSO-VMD information Article 1 1 2 1 1 3 , Ziqi Peng , Hongzi Bai , Tatsuo Shiina , Jianglong Deng , Bei Liu and Xian Zhang * College of Mathematics and Physics, Hunan University of Arts and Science, Changde 415000, China Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan School of Geosciences and Info-Physics, Central South University, Changsha 410083, China * Correspondence: [email protected]; Tel.: +86-731-8887-2258 Abstract: LED (light-emitting diode)-lidar (light detection and ranging) has gradually been focused on by researchers because of its characteristics of low power, high stability, and safety to human eyes. However, LED-lidar systems are easily disturbed by background light noise. Echo signal denoising is an essential work that directly affects the measurement accuracy of the LED-lidar system. The traditional variational modal decomposition (VMD) method in lidar signal denoising relies on practical experience to optimize the critical parameters of quadratic penalty factor and the number of intrinsic mode function (IMF) components K globally, which is hard to denoise effectively. For this problem, a denoising method based on VMD with the adaptive weighted particle swarm optimization (PSO) is proposed in this work. The PSO-VMD method adaptively adjusts the weight value ! for different lidar echo signals and optimizes of the parameters and K globally. The LED-lidar echo signals are denoised by moving average, VMD, and PSO-VMD. Using the denoised echo signals, the range compensation waveforms and the extinction coefficients are derived. The results show that the PSO-VMD denoised echo signal has the highest R-square value of 0.9972 and the minimum standard deviation value of 5.7369, while the values of r-square and standard deviation of the echo signal denoised by moving average and VMD method are 0.9902, 9.7450, 0.9945, and 7.3588, respectively. The derived distance compensation waveforms and extinction coefficients based on the PSO-VMD denoising have better stability than those based on the moving average and VMD denoising. Citation: Peng, Z.; Bai, H.; Shiina, T.; Keywords: LED-lidar; denoising; variational modal decomposition; particle swarm optimization Deng, J.; Liu, B.; Zhang, X. LED-Lidar Echo Denoising Based on Adaptive PSO-VMD. Information 2022, 13, 558. https://doi.org/10.3390/info13120558 1. Introduction Academic Editor: Zahir M. Hussain As a typical optical remote sensing technology [1], lidar (light detection and rang- ing) is widely applied in environmental monitoring, geographic mapping, hazardous gas Received: 25 July 2022 detection, and other applications [2–11]. With the development of industrialization and Accepted: 26 November 2022 the increasingly severe global environmental problems, the environmental monitoring Published: 29 November 2022 applications of lidar, especially atmospheric aerosol monitoring, have been widely studied Publisher’s Note: MDPI stays neutral by researchers. Compared with chemical sensor measurement techniques, lidar has the with regard to jurisdictional claims in advantages of a wide measurement range, high accuracy, and the ability to obtain the published maps and institutional affil- spatial distribution of the aerosol by scanning. These advantages benefit from the collima- iations. tion and high-power characteristics of the laser light source. However, the high-quality laser is expensive, bulky, has a high power consumption, and is strict for the use of the environment. More importantly, the use of high-power lasers in the central part of the city, urban buildings, and densely populated spaces has safety risks to human eyes. These Copyright: © 2022 by the authors. factors make lidar mainly used in developed countries or advanced regions, and its use Licensee MDPI, Basel, Switzerland. environment is limited in laboratories and sparsely populated areas. Lidar is challenging to This article is an open access article be applied in densely populated areas of cities for various types of monitoring applications. distributed under the terms and The safety of the light source, the compactness of the lidar device, and the power conditions of the Creative Commons consumption are essential factors in close- and small-range aerosol monitoring applications, Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ such as dust monitoring on factory floors, exhaust gas emission monitoring in factories, 4.0/). flammable and explosive gas monitoring in hydrogen energy station, etc. For these reasons, Information 2022, 13, 558. https://doi.org/10.3390/info13120558 https://www.mdpi.com/journal/information Information 2022, 13, 558 2 of 14 this study focuses on the lidar system with LED (light-emitting diode) as the light source. Although LED is inferior to laser in terms of collimation, emission power, and spectral line width, it has many advantages that lasers do not have: low price, low energy consumption, low-voltage working power, high stability, high applicability, high flexibility in application, and safety to human eyes. For these advantages, LED is widely applied in various scenarios. The Shiina’s group from Chiba University started the application of LED-lidar ear- lier. Several prototypes such as in-line-type and dual-axis-type LED-lidar were created by their team [12,13]. Their team applied the LED-lidar system in surface atmospheric measurements and successfully acquired close-range atmospheric echo signals. However, the LED light source is difficult to collimate, and its radiated power decreases rapidly with increasing distance, which makes the LED-lidar system vulnerable to the influence of background light noise. It is challenging to meet the high-precision measurement in spatial resolution and dynamic range. To improve the applicability of LED-lidar in various applications, echo signal denoising is vital work. However, the difference in power and collimation between LED-lidar and traditional lidar makes the dynamic range of LED-lidar echo signal much smaller than that of traditional lidar. The simple denoising method, such as moving average, cannot remove the noise of LED-lidar echo well, even wrongly removing the LED-lidar echo signal as background noise. Therefore, an effective denoising method can improve the accuracy of aerosol monitoring with LED-lidar, especially in long distances with a low value of signal-to-noise ratio (SNR). The lidar echo is a nonlinear and nonstationary signal. Nonlinear denoising algorithms such as Kalman filter (KF), wavelet transform (WT), empirical mode decomposition (EMD), and other algorithms have been applied in the application of lidar denoising. KF is a recur- sive algorithm based on minimum mean square error, which can process nonstationary and multidimensional signals from time-varying systems. However, the calculation accuracy of this method decreases significantly when the signals change dramatically [14]. WT can decompose signals into different frequency components through multiscale analysis, which has good localization characteristics in the time–frequency domain. However, it has poor adaptability due to the selection of the wavelet basis function [15]. EMD made up for the inadequacy of WT, which has good adaptability and can reflect the characteristics of the specific frequency of the signal. However, it has the endpoint effect and modal aliasing problems due to the recursive mode decomposition characteristics of the EMD method, which hinders the separation of the echo signal from noise [16,17]. For these reasons, variational mode decomposition (VMD) is proposed to solve the problem above. VMD can effectively avoid the problems of modal aliasing and endpoint effect caused by EMD. However, it is found that the quadratic penalty factor a and the number of intrinsic mode function (IMF) components K have a significant influence on its decomposition effect [18]. The traditional VMD method combines the local optimal solution of and K by experimental method and empirical method, respectively [19]. However, the combination of local optimal solutions is challenging to achieve the global optimal effect because of the correlation between and K parameters. To increase the denoising effect of VMD in LED-lidar applications, an algorithm that can optimize critical parameter combinations [ , K] is needed [20]. Particle swarm optimization (PSO) is an intelligent algorithm with global optimization ability [21]. The algorithm finds the optimal solution through cooperation and information sharing among individuals in a group. It has been widely used in function optimization, neural network training, fuzzy system control, and other applications of genetic algorithms due to its simple operation and fast convergence [22,23]. However, for traditional PSO, it is difficult to achieve local optimization and global optimization synchronously because the weight parameter ! is set as a constant. It can obtain a better global optimization effect if the ! can be assigned dynamically in different original signals. In this paper, the parameters [ , K] of VMD are optimized by the PSO algorithm with adaptive weights, and the VMD is used to denoise the LED-lidar echo signals. To estimate the effectiveness of the PSO-VMD algorithm, the same LED-lidar atmospheric Information 2022, 13, 558 3 of 14 echo signals are denoised with the moving average method, the VMD algorithm, and the PSO-VMD algorithm, respectively, and the denoised results are compared. The improved effect of denoising from the PSO-VMD is also estimated from the calculation result of the extinction coefficient. The main content of this paper is as follows: Section 1 presents the background of LED- lidar and the algorithm of lidar signal denoising. Section 2 offers the PSO-VMD method. Section 3 introduces the LED-lidar system, data acquisition, and calculation process of extinction coefficient. Section 4 presents the results of LED-lidar signal denoising with PSO-VMD and the other methods. Section 5 is the conclusion. 2. Theory 2.1. VMD VMD is a new multicomponent signal decomposition algorithm based on Wiener filtering, Hilbert transform, and outlier demodulation [18]. VMD can decompose a signal f (t) into K discrete modes m (k = 1, 2, 3 , K). m are amplitude–frequency modulated k k (AM-FM) signals, and their bandwidths have sparsity in the frequency domain, effectively suppressing the modal aliasing that occurs in EMD. Each m is compacted around the center frequency, and its bandwidth can be obtained by Gaussian smoothing demodulation. The constrained variational problem in the VMD can be expressed as: 8 8 99 < < h  i == jw t 2 min ¶ d(t) + m (t) e å k 2 pt : : ;; fm g,fw g k k k (1) S.t. m (t) = f fm g = fm , m  m g and fw g = fw , w w g are the sets of the decomposed 2 2 k 1 K k 1 K modes and their central frequencies, respectively. The quadratic penalty parameter a and the Lagrange multiplier operator l(t) are introduced to obtain the solution to the constrained variational problem in Equation (1). The augmented Lagrangian function is expressed as: h  i jw t 2 L m , w , l = a ¶ d(t) +  m (t) e (f g f g ) k k t k pt 2 (2) + f (t) m .(t) + l(t), f (t) m (t) å k å k k k The saddle point of Equation (2) can be obtained by the alternating direction method of multipliers. Then m , w , and l can be updated iteratively in the frequency domain. k k The steps of VMD are as follows: 1 1 1 (a) Initializing m , w , l and setting n = 0; k k (b) Updating m and w iteratively by Equations (3) and (4), respectively: k k l(w) f (w) m (w) + i6=k n+1 2 m (w) = (3) 1 + 2a(w w ) ¥ 2 wjm (w)j dw n+1 0 w = R (4) k ¥ jm (w)j dw (c) Updating l according to Equation (5): 2 3 n+1 n n+1 4 5 l (w) l (w) + t f (w) m (w) (5) k Information 2022, 13, 558 4 of 14 (d) Repeating steps (b)–(c) until the iteration result is satisfied the ending condition: n+1 n 2 n 2 km m k /km k < # (6) å k 2 k 2 where # is the discriminant accuracy, and # > 0. (e) Outputting K modal components. 2.2. PSO PSO is an algorithm for global optimization of key parameters, and determination of the fitness function is a key step in the PSO algorithm [21]. The fitness function is updated with the change in particle position, and the updated direction of the particle is dependent on the value of the fitness function. The minimum of the envelope entropy is used as the fitness function, which represents the sparsity of the original signal. The envelope entropy is more prominent when the signal-to-noise power ratio is small. On the other hand, the envelope entropy value is smaller when the signal-to-noise power ratio is significant. The envelope entropy E can be expressed as: E = p lg p (7) p å j j j=1 a(j) p = (8) j=1 2 2 a(j) = x (j) + x (j) (9) where p is the sequence of probability distributions of a(j); a(j) is the envelope obtained from the Hilbert demodulation of x(j). The weight parameter ! in the traditional PSO algorithm is set as a constant, which easily leads to the problem of local optima. An adaptive nonlinear dynamic inertial weight coefficient !, as shown in Equation (10), was adopted in the PSO algorithm to optimize the VMD parameters in this study. The flowchart of the adaptive-weight PSO-VMD is shown in Figure 1. The nonlinear dynamic inertial weight is closely related to the global optima, which can vary with the position of particles, and solve the problem of local optima. (w w ) f f max ( avg) min w , f  f avg min f f avg w = min (10) w , f > f max avg where f is the fitness function, which is E mentioned in Equation (7); f is the average of p avg the fitness function; and f is the minimum of the fitness function. min The calculation steps of PSO-VMD are as follows: (a) Parameter initialization: the main parameters are the population size, the maximum number of iterations, and the search range of the parameters and K. (b) Updating iteratively: using the minimum of envelope entropy as the fitness function and updating the velocity and position of the population iteratively. (c) Determining the adaptive nonlinear dynamic inertial weight ! according to the most calculated current envelope entropy and the mean value of envelope entropy. (d) Update the new optimal [ , K] and the minimum envelope entropy if the new calcu- lated envelope entropy is smaller than the minimum of the envelope entropy. (e) Repeat steps (b)–(d) until the maximum number of iterations as well as the minimum envelope entropy is determined; output the optimal parameters and K. Information Information2022 2022 ,,13 13 ,, x FOR PEER 558 REVIEW 5 of 5 of 14 14 Figure 1. Flowchart of the adaptive-weight particle swarm optimization (PSO) - variational modal Figure 1. Flowchart of the adaptive-weight particle swarm optimization (PSO) - variational modal decomposition (VMD). decomposition (VMD). 3. LED-Lidar System and Signal Processing The calculation steps of PSO-VMD are as follows: 3.1. LED-Lidar System (a) Parameter initialization: the main parameters are the population size, the maximum A biaxial type of LED-lidar was used in this study [13]. Figure 2 shows the schematic number of iterations, and the search range of the parameters α and K. diagram of LED-lidar and its prototype used in this study. The LED pulse driver provides (b) Updating iteratively: using the minimum of envelope entropy as the fitness function a pulse with a high frequency of 500 kHz and a pulse width of 10 ns, which is used to and updating the velocity and position of the population iteratively. drive a high-power LED with a wavelength of 395 nm. The LED has an average power of (c) Determining the adaptive nonlinear dynamic inertial weight ω according to the most 3.82 mW and a peak power of 764 mW. The beam from LED is collimated by a combination calculated current envelope entropy and the mean value of envelope entropy. of a silicone lens and a Fresnel lens and emitted from the transmitter with a diffusion angle (d) Update the new optimal [α, K] and the minimum envelope entropy if the new calcu- of 12.5 mrad. The transmitted beam generates the backscattering light while propagating lated envelope entropy is smaller than the minimum of the envelope entropy. in the aerosol. The backscattering light is focused by the telescope and collimating lens. (e) Repeat steps (b)–(d) until the maximum number of iterations as well as the minimum After filtering with a special filter and bandpass filter, the focused light is converted to envelope entropy is determined; output the optimal parameters α and K. electrical signals by a photomultiplier tube (PMT). The photon counter is used for the integral operation to make the LED-lidar echo signal stable. The LED-lidar echo samples 3. LED-Lidar System and Signal Processing used in this study are obtained from the photon counter with 10 integrals. 3.1. LED-Lidar System A biaxial type of LED-lidar was used in this study [13]. Figure 2 shows the schematic diagram of LED-lidar and its prototype used in this study. The LED pulse driver provides a pulse with a high frequency of 500 kHz and a pulse width of 10 ns, which is used to drive a high-power LED with a wavelength of 395 nm. The LED has an average power of 3.82 mW and a peak power of 764 mW. The beam from LED is collimated by a combina- tion of a silicone lens and a Fresnel lens and emitted from the transmitter with a diffusion angle of 12.5 mrad. The transmitted beam generates the backscattering light while propa- gating in the aerosol. The backscattering light is focused by the telescope and collimating Information 2022, 13, x FOR PEER REVIEW 6 of 14 lens. After filtering with a special filter and bandpass filter, the focused light is converted to electrical signals by a photomultiplier tube (PMT). The photon counter is used for the Information 2022, 13, 558 6 of 14 integral operation to make the LED-lidar echo signal stable. The LED-lidar echo samples used in this study are obtained from the photon counter with 10 integrals. (a) (b) Figure 2. LED-lidar system: (a) schematic diagram; (b) prototype. Figure 2. LED-lidar system: (a) schematic diagram; (b) prototype. 3.2. Lidar Echo Signal and Signal Processing 3.2. Lidar Echo Signal and Signal Processing The analysis of LED-lidar echo signal is based on the lidar equation [24]: The analysis of LED-lidar echo signal is based on the lidar equation [24]: 𝑐𝜏 1 ct 1 (11) 𝑃 𝑟 =𝑃 ∙𝐾 ∙𝑌 𝑟 ∙ 𝐴 ∙ ∙𝛽 𝑟 ∙ ∙exp 2𝜎𝑟 P(r) = P KY(r) A  b(r)  exp(2sr) (11) 2 𝑟 2 r where 𝑟 is the measurement distance; 𝑃 𝑟 is the received power; 𝑃 is the transmitted where r is the measurement distance; P(r) is the received power; P is the transmitted power; 𝐾 is the system efficiency determined by the optical system of LED-lidar; 𝑌 is the power; K is the system efficiency determined by the optical system of LED-lidar; Y is the geometric overlap coefficient, representing the overlap rate of the field of view between geometric overlap coefficient, representing the overlap rate of the field of view between receiver and transmitter, which is determined by the angle of view of transmitter and re- receiver and transmitter, which is determined by the angle of view of transmitter and ceiver; 𝐴 is the receiving area of the receiver determined by the aperture of the telescope; receiver; A is the receiving area of the receiver determined by the aperture of the telescope; 𝑐 is the speed of light; 𝜏 is the pulse width of light; 𝛽 is the atmospheric backscattering c is the speed of light; t is the pulse width of light; b is the atmospheric backscattering coefficient; and 𝜎 is atmospheric extinction coefficient. coefficient; and s is atmospheric extinction coefficient. Figure 3 shows the backscattering echo signals from atmospheric aerosols obtained Figure 3 shows the backscattering echo signals from atmospheric aerosols obtained by by LED-lidar. The x-axis is the distance derived from the flight time of the photon. The y- LED-lidar. The x-axis is the distance derived from the flight time of the photon. The y-axis axis is the intensity of the LED-lidar echo signal with the unit of count. At a distance of is the intensity of the LED-lidar echo signal with the unit of count. At a distance of about about 17 m, the geometric overlap coefficient of the system approaches 1, and the echo 17 m, the geometric overlap coefficient of the system approaches 1, and the echo signal of signal of atmospheric aerosol decreases exponentially with the increase in distance. As the atmospheric aerosol decreases exponentially with the increase in distance. As the geometric overlap coefficient increases gradually from 0 in the near distance, the backscattering echo shows an increasing trend in the close space. The maximum signal in the waveform is the point where the field overlap rate of the transmitter and receiver reaches the top. The geometric overlap coefficient reaches the top. Only the part of the signal farther than the Information 2022, 13, 558 7 of 14 maximum point can effectively evaluate the optical properties of atmospheric aerosol. The echo signal contains harmonic noise carried from the pulse modulation process. Due to the short pulse width of 10 ns and the precision of the modulation circuit, it is easy to form unstable harmonics, which become a part of the echo noise after being amplified by the LED driver. The background light is another kind of echo noise. Especially for the echo with low intensity obtained from a far distance, it is more susceptible to the influence of background light. 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 50 100 150 200 250 300 Distance (m) Figure 3. A typical backscattering echo signals from atmospheric aerosols. Atmospheric extinction coefficient s is an important parameter used to evaluate the optical characteristics of atmospheric aerosol. Although the atmospheric extinction coeffi- cient has a spatial distribution, it is difficult to find the reference of the spatial distribution of the extinction coefficient on the surface to evaluate the denoising effect. Therefore, the average atmospheric extinction coefficient within a period of time is used as a reference to evaluate the denoising effect. The most classical slope method [25] is adopted to derive the parameter s. The deriving process of s is as follows: (a) Carrying out the product operation of r for both sides of the lidar equation. (b) Taking the natural logarithm for both sides of the equation. (c) Taking the derivative of r for both sides of the equation. As the parameters P , K, Y(r), A , c, and t are constant, the new equation can be 0 r written as: d ln P(r)r 1 db(r) =  2s (12) dr b(r) dr Considering that the atmosphere is homogeneous, and the backscattering coefficient b is a constant, then db(r)/dr = 0. The homogeneous atmospheric extinction coefficient can be expressed in the following form: d ln P(r)r s (r) =  (13) 2 dr According to Equation (12), compensating the echo signal by multiplication of r , and taking the natural logarithm, the extinction coefficient can be derived as 1/2 of the slope of the compensated waveform, which is formed by the function of ln P(r)r . Lidar echo (count) Information 2022, 13, x FOR PEER REVIEW 8 of 14 Information 2022, 13, 558 8 of 14 Figure 4 shows the waveform of the LED-lidar echo after range compensation. Due Figure 4 shows the waveform of the LED-lidar echo after range compensation. Due to the low signal intensity of the long-range echo, the compensated echo signal is easily to the low signal intensity of the long-range echo, the compensated echo signal is easily affected by the background light noise. After the range compensation, the background affected by the background light noise. After the range compensation, the background light light noise at the long range is further amplified, making the signal at the long range un- noise at the long range is further amplified, making the signal at the long range unstable. stable. The slope of the middle and rear waveform is calculated as the extinction coeffi- The slope of the middle and rear waveform is calculated as the extinction coefficient. The cient. The red dashed line is a linear fitted line obtained from the part of the range com- red dashed line is a linear fitted line obtained from the part of the range compensation signal, pensation signal, which is further than 100 m, and 1/2 of its slope is the extinction coeffi- which is further than 100 m, and 1/2 of its slope is the extinction coefficient characterized cient characterized by the LED-lidar. The instability of the signal at the long range is prone by the LED-lidar. The instability of the signal at the long range is prone to error in the to error in the process of the linear fit, especially when batch processing large amounts of process of the linear fit, especially when batch processing large amounts of LED-lidar echo LED-lidar echo data. Therefore, for the high-accuracy linear fit of the range compensation data. Therefore, for the high-accuracy linear fit of the range compensation signal, effective signal, effective LED-lidar echo denoising is an indispensable work in this study. LED-lidar echo denoising is an indispensable work in this study. 15.8 linear fitted (red dashed line) 15.6 15.4 15.2 14.8 14.6 14.4 14.2 0 50 100 150 200 250 300 Distance (m) Figure 4. Figure 4.LED- LED-lidar lidar eecho cho wave waveform form after range compensation. after range compensation. 4. Result 4. Result 4.1. Denoising of LED-Lidar Echo 4.1. Denoising of LED-Lidar Echo The moving average, VMD, and PSO-VMD are used to denoise the atmospheric aerosol The moving average, VMD, and PSO-VMD are used to denoise the atmospheric aer- echo signals of the LED-lidar. The denoising results are shown in Figure 5. Figure 5a–c osol echo signals of the LED-lidar. The denoising results are shown in Figure 5. Figure 5a– shows the denoising results using moving average, VMD, and PSO-VMD, respectively, and c show the denoising results using moving average, VMD, and PSO-VMD, respectively, the details of the waveform in the interval from 100 m to 300 m are shown in the box on and the details of the waveform in the interval from 100 m to 300 m are shown in the box the right side of the figure. Figure 5d shows the comparison of the denoising effect of the on the right side of the figure. Figure 5d shows the comparison of the denoising effect of three methods. In Figure 5a, the result of the denoised echo is based on the 5-point moving the three methods. In Figure 5a, the result of the denoised echo is based on the 5-point average, which shows that the moving average method can effectively suppress the noise moving average, which shows that the moving average method can effectively suppress and make the echo signal smooth partly. The longer the moving average length, the better the noise and make the echo signal smooth partly. The longer the moving average length, the noise suppression effect. However, the information is easily lost if the average length is the better the noise suppression effect. However, the information is easily lost if the aver- set as a large value. Due to the steep gradient of signal intensity in the peak region, part age length is set as a large value. Due to the steep gradient of signal intensity in the peak of the information in the peak region is lost after moving average denoising, which is the region, part of the information in the peak region is lost after moving average denoising, disadvantage of the moving average method. Figure 5b shows the denoising results of the which is the disadvantage of the moving average method. Figure 5b shows the denoising VMD with the empirical parameters [ = 200, K = 5]. The selection of parameters [ , K] results of the VMD with the empirical parameters [α = 200, K = 5]. The selection of param- is crucial in VMD denoising. For the same set of data, different parameter selection can eters [α, K] is crucial in VMD denoising. For the same set of data, different parameter achieve other denoising effects. Similarly, for the same set of empirical parameters [ , K], selection can achieve other denoising effects. Similarly, for the same set of empirical pa- different denoising effects can be obtained when processing other data. Compared with rameters [α, K], different denoising effects can be obtained when processing other data. the moving average method, the VMD method not only overcomes the disadvantage of the C information ompared wloss ith the m brought oviby ng av theer moving age meaverage thod, the method VMD m due ethod no to a long t onl moving y overco average mes the but disadvantage of the information loss brought by the moving average method due to a also better suppresses the signal fluctuations in the region of low intensity. Figure 5c shows long mov the denoising ing ar vesults erage but based also bet on PSO-VMD. ter suppresse As the s the sign initialization al flucof tua PSO, tions in the the article region swarm of low sizeint is e set nsias ty.10, Figur maximum e 5c shows iterations the deno number ising res isu set lts as based 10, on and PS minimum O-VMD. As fitness the in value itialiis - set as 0.001. Thanks to the parameter optimization of PSO, the denoised echo signal not zation of PSO, the article swarm size is set as 10, maximum iterations number is set as 10, only maintains the same intensity level as the original echo signal but also finely rejects the ln( p(r) * r )(a.u.) Information 2022, 13, x FOR PEER REVIEW 9 of 14 and minimum fitness value is set as 0.001. Thanks to the parameter optimization of PSO, Information 2022, 13, 558 9 of 14 the denoised echo signal not only maintains the same intensity level as the original echo signal but also finely rejects the subtle noise. The denoised echo signal is smoother than the one obtained by the empirical parameters of VMD. Figure 5d shows the comparison subtle noise. The denoised echo signal is smoother than the one obtained by the empirical of the three methods of denoising results in the region of 100–300 m. The moving average parameters of VMD. Figure 5d shows the comparison of the three methods of denoising denoising not only has information loss but also cannot suppress the signal fluctuation results in the region of 100–300 m. The moving average denoising not only has information caused by the noise. The PSO-VMD has the best performance in signal denoising and fluc- loss but also cannot suppress the signal fluctuation caused by the noise. The PSO-VMD has tuation suppressing. the best performance in signal denoising and fluctuation suppressing. 10,000 10,000 Original lidar echo Original lidar echo 9000 9000 Moving average denoising VMD denoising 8000 8000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Distance (m) Distance (m) (a) (b) 10,000 450 Moving average denoising Original lidar echo VMD denoising PSO-VMD denoising 390 PSO-VMD denoising 0 30 0 50 100 150 200 250 300 100 140 180 220 260 300 Distance (m) Distance (m) (c) (d) Figure 5. Denoising result of LED-lidar echo: (a) moving average; (b) VMD; (c) PSO-VMD; (d) com- Figure 5. Denoising result of LED-lidar echo: (a) moving average; (b) VMD; (c) PSO-VMD; parison of (a–c). (d) comparison of (a–c). In the measurement of atmospheric aerosols, the ideal lidar echo should be close to In the measurement of atmospheric aerosols, the ideal lidar echo should be close to the exponential attenuation when the distribution of aerosols is uniform, and the geomet- the exponential attenuation when the distribution of aerosols is uniform, and the geometric ric overlap coefficient of the lidar system is 1. Fifty samples are selected from the denoising overlap coefficient of the lidar system is 1. Fifty samples are selected from the denoising signals obtained by the three different methods and the original echo signal, respectively. signals obtained by the three different methods and the original echo signal, respectively. The 100–300 m range of the signal was selected and fitted exponentially. The average R- The 100–300 m range of the signal was selected and fitted exponentially. The average square and root mean squared error (RMSE) were calculated. The calculation results are R-square and root mean squared error (RMSE) were calculated. The calculation results are shown in Table 1 The R-square represents the similarity between the experimental signal shown in Table 1 The R-square represents the similarity between the experimental signal and the ideal fitted signal. The closer the value is to 1, the closer the experimental signal and the ideal fitted signal. The closer the value is to 1, the closer the experimental signal is to the ideal fitted signal. Compared with the original echo signal before denoising, the is to the ideal fitted signal. Compared with the original echo signal before denoising, the R- R-squar square va e values lues of of the deno the denoised ised sisignals gnals ar ar e sign e significantly ificantly improved, e improved, s especially pecially for for th the e PSO- PSO- VMD denoising, the R-square value reaches the highest value of 0.9972. RMSE re VMD denoising, the R-square value reaches the highest value of 0.9972. RMSE repr presents esents the the dev deviation iation bbetween etween th the e eexperimental xperimental ssignal ignal an and d the the ide ideal al fi fitted tted si signal. gnal. The sm The smaller aller th the e value is, th value is, the e closer closer the expe the experimental rimental sign signal al is to the is to the idea ideal l fitted s fitted igna signal. l. Com Compar pared with ed with the the original signal before denoising, the RMSE of the signal after denoising decreased original signal before denoising, the RMSE of the signal after denoising decreased signif- significantly, especially the RMSE of the PSO-VMD denoising result, which reaches the icantly, especially the RMSE of the PSO-VMD denoising result, which reaches the mini- minimum value of 5.7369. Although the optimization parameters based on experience were mum value of 5.7369. Although the optimization parameters based on experience were used in VMD denoising, due to the difference between signals caused by the random error of measurement environment and background light, it is difficult to achieve the optimal denoising of all data with the optimization parameters based on experience. Comparing Lidar echo (count) Lidar echo (count) Lidar echo (count) Lidar echo (count) Information 2022, 13, x FOR PEER REVIEW 10 of 14 used in VMD denoising, due to the difference between signals caused by the random error of measurement environment and background light, it is difficult to achieve the optimal denoising of all data with the optimization parameters based on experience. Comparing the R-Square and RMSE values of VMD and PSO-VMD, it shows that PSO has a significant optimization effect on VMD in LED-lidar denoising. Information 2022, 13, 558 10 of 14 Table 1. Comparison of R-square and RMSE with the three denoising methods. Denoising Method R-Square RMSE the R-Square and RMSE values of VMD and PSO-VMD, it shows that PSO has a significant Original echo 0.9421 24.0928 optimization effect on VMD in LED-lidar denoising. Moving average 0.9902 9.7450 VMD 0.9945 7.3588 Table 1. Comparison of R-square and RMSE with the three denoising methods. PSO-VMD 0.9972 5.7369 Denoising Method R-Square RMSE Original echo 0.9421 24.0928 4.2. Range Compensation Moving average 0.9902 9.7450 VMD 0.9945 7.3588 As mentioned in Section 3.2, before solving the extinction coefficient of the LED-lidar PSO-VMD 0.9972 5.7369 aerosol echo signal with the slope method, the range compensation is required. However, as the distance increases, the compensated value to the echo signal gradually increases, 4.2. Range Compensation and the noise is also amplified by the multiplication of range compensation. The signal- As mentioned in Section 3.2, before solving the extinction coefficient of the LED-lidar to-noise ratio of the distant echo signal is smaller than that of the near echo signal, which aerosol echo signal with the slope method, the range compensation is required. However, leads to increasing fluctuations in the range compensation as the distance increases. The as the distance increases, the compensated value to the echo signal gradually increases, fluctuation and the of the r noise is a also nge ampli compensation b fied by the multiplication rings a significant error of range compensation. to calculating The signal- the slope by to-noise ratio of the distant echo signal is smaller than that of the near echo signal, which a linear fit. The range compensation was carried out after denoising the original echo sig- leads to increasing fluctuations in the range compensation as the distance increases. The nal of LED-lidar by moving average, VMD, and PSO-VMD, respectively. The calculation fluctuation of the range compensation brings a significant error to calculating the slope results are shown in Figure 6. Figure 6a–c show the range compensation results by using by a linear fit. The range compensation was carried out after denoising the original echo the denoised signal to deal with the moving average method, VMD, and PSO-VMD, re- signal of LED-lidar by moving average, VMD, and PSO-VMD, respectively. The calculation spectively. Comparing the range compensation results of the echo signal after denoising results are shown in Figure 6. Figure 6a–c show the range compensation results by using by the the th denoised ree methods signal wi totdeal h that with of th the e origin moving alaverage signal, method, the fluctu VMD, ation of and the d PSO-VMD, istant signal respectively. Comparing the range compensation results of the echo signal after denoising is suppressed. The denoising process removes part of the noise in the distant signal with by the three methods with that of the original signal, the fluctuation of the distant signal low SNR, which reduces the noise amplification from the range compensation. Figure 6d is suppressed. The denoising process removes part of the noise in the distant signal with compares the range compensation results denoised by the three methods. Compared with low SNR, which reduces the noise amplification from the range compensation. Figure 6d the moving average method, the range compensation result of VMD denoising has some compares the range compensation results denoised by the three methods. Compared improvement in suppressing fluctuation. However, the effect is not apparent, since IMF with the moving average method, the range compensation result of VMD denoising has some improvement in suppressing fluctuation. However, the effect is not apparent, since components K determined empirically is not the optimal value. On the other hand, com- IMF components K determined empirically is not the optimal value. On the other hand, pared with the VMD denoising, the PSO-VMD denoised range compensated signal is sig- compared with the VMD denoising, the PSO-VMD denoised range compensated signal nificantly improved in signal fluctuation. The high-frequency components from back- is significantly improved in signal fluctuation. The high-frequency components from ground noise and white noise are also suppressed, which is the effect of the critical pa- background noise and white noise are also suppressed, which is the effect of the critical rameters of K and α optimized by the PSO. parameters of K and optimized by the PSO. 16 16 Range compensation without denoising Range compensation without denoising 15.8 15.8 Moving average range compensation VMD range compensation 15.6 15.6 15.4 15.4 15.2 15.2 14.8 14.8 14.6 14.6 14.4 14.4 14.2 14.2 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Distance (m) Distance (m) (a) (b) Figure 6. Cont. ln( p(r) * r ) (a.u.) ln( p(r) * r ) (a.u.) Information 2022, 13, x FOR PEER REVIEW 11 of 14 Information 2022, 13, 558 11 of 14 16 15.6 Moving average range compensation Range compensation without denoising 15.8 VMD range compensation PSO-VMD range compensation 15.5 PSO-VMD range compensation 15.6 15.4 15.4 15.2 15 15.3 14.8 15.2 14.6 14.4 15.1 14.2 14 15 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Distance (m) Distance (m) (c) (d) Figure 6. LED-lidar echo range compensation: (a) moving average; (b) VMD; (c) PSO-VMD; (d) Figure 6. LED-lidar echo range compensation: (a) moving average; (b) VMD; (c) PSO-VMD; comparison of (a–c). (d) comparison of (a–c). 4.3. Extinction Coefficient 4.3. Extinction Coefficient A set of LED-lidar echoes containing 196 samples was denoised with moving average, A set of LED-lidar echoes containing 196 samples was denoised with moving aver- VMD, and PSO-VMD, and the extinction coefficients at different time points were derived. age, VMD, and PSO-VMD, and the extinction coefficients at different time points were The samples were acquired on the night of 26 March 2019 (cloudy) in the city of Changde. derived The. The LED-lidar sample was s wer set on e ac the quired 6th floor on of the nigh the second t of laboratory 26 March building 2019 (cloud of the y) Hunan in the city of University of Arts and Sciences, with an elevation angle of 60 . The period of sample Changde. The LED-lidar was set on the 6th floor of the second laboratory building of the acquisition was from 19:27 to 21:24. The number of data integration times was set as 10 Hunan University of Arts and Sciences, with an elevation angle of 60°. The period of sam- (mentioned in Section 3.1), and the acquisition time of each sample was about 40 s. ple acquisition was from 19:27 to 21:24. The number of data integration times was set as Figure 7 shows the extinction coefficients derived from the data in the region of 10 (mentioned in Section 3.1), and the acquisition time of each sample was about 40 s. 100–300 m, which was denoised by the moving average, VMD, and PSO-VMD. For all Figure 7 shows the extinction coefficients derived from the data in the region of 100– the samples, the PSO initialization was set as the parameters mentioned in Section 4.1. The x-axis is the time point, and the y-axis is the extinction coefficient. Although the 300 m, which was denoised by the moving average, VMD, and PSO-VMD. For all the calculation region and the elevation angle of LED-lidar were set as constant, the extinction samples, the PSO initialization was set as the parameters mentioned in Section 4.1. The x- coefficients derived by three methods fluctuated by varying degrees. The instability of the axis is the time point, and the y-axis is the extinction coefficient. Although the calculation extinction coefficient is influenced by the flow of surface–atmosphere and variations of region and the elevation angle of LED-lidar were set as constant, the extinction coefficients surface urban environmental conditions. On the other hand, the nonlinear signal itself, the derived by three methods fluctuated by varying degrees. The instability of the extinction influence of noise, and the poor adaptability of the fitting algorithm are also the reasons coefficient is influenced by the flow of surface–atmosphere and variations of surface ur- causing the extinction coefficients to fluctuate. According to Lambert Beer ’s law, the extinction coefficient, in theory, should be negative values because of the light scattering ban environmental conditions. On the other hand, the nonlinear signal itself, the influence in the atmosphere when light propagates in the atmosphere. However, some extinction of noise, and the poor adaptability of the fitting algorithm are also the reasons causing the coefficients with positive values were still obtained in this study. Due to the intense extinction coefficients to fluctuate. According to Lambert Beer’s law, the extinction coeffi- background light appearing in some data samples, even the excellent PSO-VMD method cient, in theory, should be negative values because of the light scattering in the atmos- could not remove the noise at a long distance, which leads to the fact that as the noise is phere when light propagates in the atmosphere. However, some extinction coefficients amplified in the process of range compensation, the range compensated signal intensity with positive values were still obtained in this study. Due to the intense background light at a long distance is higher than that at a short distance. The slope of the linear fitting becomes a positive value. Compared with the derived extinction coefficients by moving appearing in some data samples, even the excellent PSO-VMD method could not remove average and VMD method, the number of positive values of extinction coefficients derived the noise at a long distance, which leads to the fact that as the noise is amplified in the by the PSO-VMD method is only 4, which is the least. The result indicates that the PSO- process of range compensation, the range compensated signal intensity at a long distance VMD method can remove the noise from background light more effectively. The standard is higher than that at a short distance. The slope of the linear fitting becomes a positive deviations of the extinction coefficients derived by moving average, VMD, and PSO-VMD 4 4 4 value. Compared with the derived extinction coefficients by moving average and VMD were calculated, and the values were 5.7452  10 , 4.7309  10 , and 2.2896  10 , method, respectively the nu.m Due ber o to f the posuperiorit sitive valu y of esPSO-VMD of extinction denoising, coefficien the fluctuation ts derived b of y extinction the PSO-VMD coefficients obtained by PSO-VMD is minimal. method is only 4, which is the least. The result indicates that the PSO-VMD method can remove the noise from background light more effectively. The standard deviations of the extinction coefficients derived by moving average, VMD, and PSO-VMD were calculated, −4 −4 −4 and the values were 5.7452 × 10 , 4.7309 × 10 , and 2.2896 × 10 , respectively. Due to the superiority of PSO-VMD denoising, the fluctuation of extinction coefficients obtained by PSO-VMD is minimal. ln( p(r) * r ) (a.u.) ln( p(r) * r ) (a.u.) Information 2022, 13, x FOR PEER REVIEW 12 of 14 Information 2022, 13, 558 12 of 14 2.0E-3 -3 2.0×10 By Moving Average By VMD By PSO-VMD -3 1.0×10 1.0E-3 -3 0.0×10 0.0E+0 -3 -1 -1 .0 .0× E10 -3 -2.0E-3 -3 -2.0×10 -3 -3.0×10 -3.0E-3 19:27 19:42 19:56 20:11 20:25 20:39 20:54 21:08 21:23 Time (mm:ss) Figure 7. Figure 7.The The eextinction xtinction co coef efficients of atmo ficients of atmospheric spheric ae aer rosol osolderived by thre derived by three e d denoising enoising method methods. s. To evaluate the accuracy of the extinction coefficients derived from the LED-lidar echo, To evaluate the accuracy of the extinction coefficients derived from the LED-lidar the extinction coefficients were derived from the surface visibility released by the Hunan echo, the extinction coefficients were derived from the surface visibility released by the provincial meteorological department and compared with the average values of the three Hunan provincial meteorological department and compared with the average values of sets of extinction coefficients calculated from LED-lidar echo. The conversion formula from the three sets of extinction coefficients calculated from LED-lidar echo. The conversion visibility to extinction coefficient is expressed as Equation (14): formula from visibility to extinction coefficient is expressed as Equation (14): 3.912 3.912 550 550 s =  (1 (14) 4) 𝜎= ∙ n 𝜈 l𝜆 where 𝜎 is the extinction coefficient, 𝜈 is the visibility, and 𝜆 is the wavelength of the where s is the extinction coefficient, n is the visibility, and l is the wavelength of the light light source. The visibility on March 26 was about 10 km, and the wavelength of the light source. The visibility on March 26 was about 10 km, and the wavelength of the light source source was 395 nm. According to the parameters of visibility and wavelength, the extinc- was 395 nm. According to the parameters of visibility and wavelength, the extinction coeffi- −4 −1 4 1 tion coefficient was calculated as 5.6 × 10 m . The mean values of extinction coefficients cient was calculated as 5.6  10 m . The mean values of extinction coefficients derived 4 1 −4 −1 4 −1 4 derived by moving average, VMD, and PSO-VMD were 6.7609 × 10 m , 6.4250 × 10 by moving average, VMD, and PSO-VMD were 6.7609  10 m , 6.4250  10 m , −1 4 −41−1 m , 5.7401 × 10 m , respectively. The average value of the extinction coefficient derived 5.7401  10 m , respectively. The average value of the extinction coefficient derived by by PSO-VMD is closest to the value of the extinction coefficient derived from visibility, PSO-VMD is closest to the value of the extinction coefficient derived from visibility, which which indicates the superiority of PSO-VMD in extinction coefficient calculation. indicates the superiority of PSO-VMD in extinction coefficient calculation. 5. Conclusions 5. Conclusions For the characteristics of nonlinear, low SNR, and low dynamic range in LED-lidar echo For the characteristics of nonlinear, low SNR, and low dynamic range in LED-lidar signal, a novel denoising method based on VMD with adaptive-weight PSO is proposed. echo signal, a novel denoising method based on VMD with adaptive-weight PSO is pro- Compared with the traditional VMD denoising method, this method dynamically assigns posed. Compared with the traditional VMD denoising method, this method dynamically the weights w in the PSO algorithm for the different echo signals. It globally optimizes the assigns the weights 𝜔 in the PSO algorithm for the different echo signals. It globally op- critical parameters [ , K] of VMD, which further improves the denoising effect. timizes the critical parameters [α, K] of VMD, which further improves the denoising effect. Echo signal denoising, range compensation, and extinction coefficient calculation were Echo signal denoising, range compensation, and extinction coefficient calculation performed by using moving average, VMD, and PSO-VMD, respectively. The denoised were performed by using moving average, VMD, and PSO-VMD, respectively. The de- echo signal based on PSO-VMD has the optimal R-square value of 0.9972 and the minimum noised echo signal based on PSO-VMD has the optimal R-square value of 0.9972 and the RMSE value of 5.7369. In the calculation of range compensation, the result based on PSO- minimum RMSE value of 5.7369. In the calculation of range compensation, the result VMD denoising has the slightest fluctuation at long distance. In the analysis of extinction based on PSO-VMD denoising has the slightest fluctuation at long distance. In the analysis coefficient, the extinction coefficients based on PSO-VMD denoising have the best stability. of extinction coefficient, the extinction coefficients based on PSO-VMD denoising have the Under the condition of intense background light and incomplete denoising, the number best stability. Under the condition of intense background light and incomplete denoising, of error points of slope fitting with PSO-VMD denoising is the least. The superiority of the number of error points of slope fitting with PSO-VMD denoising is the least. The su- PSO-VMD in LED-lidar denoising is proved by analysis of the three critical signals. periority of PSO-VMD in LED-lidar denoising is proved by analysis of the three critical However, a constant region and parameters were used in the calculation of linear signals. fitting, resulting in a small number of slope fitting error points when the SNR of the echo However, a constant region and parameters were used in the calculation of linear signal is low and the fluctuation is significant. In the future, the introduction of machine fitting, resulting in a small number of slope fitting error points when the SNR of the echo signal is low and the fluctuation is significant. In the future, the introduction of machine −1 Extinction Coefficient (m ) Information 2022, 13, 558 13 of 14 learning is considered, which can better perform adaptive linear fitting to further reduce the fluctuation of extinction coefficient. Author Contributions: Conceptualization, Z.P.; methodology, Z.P. and B.L.; software, B.L., X.Z. and H.B.; validation, Z.P., T.S. and J.D.; formal analysis, Z.P. and T.S.; investigation, Z.P. and H.B.; resources, X.Z.; data curation, Z.P. and B.L. writing—original draft preparation, Z.P.; writing—review and editing, Z.P.; visualization, Z.P. and T.S.; supervision, T.S.; project administration, Z.P.; funding acquisition, Z.P. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the Natural Science Youth Foundation of Hunan Province (2020JJ5396), Excellent Young Scientist Foundation of Hunan Provincial Education Department (20B405), and the Research Foundation for Advanced Talents (18BSQD32). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not Applicable, the study does not report any data. Conflicts of Interest: The authors declare no conflict of interest. References 1. Jaboyedoff, M.; Oppikofer, T.; Abellán, A.; Derron, M.; Loye, A.; Metzger, R.; Pedrazzini, A. Use of lidar in landslide investigations: A review. Nat. Hazards 2012, 61, 5–28. [CrossRef] 2. Qiu, J.; Lu, D. On lidar application for remote sensing of the atmosphere. Adv. Atmos. Sci. 1991, 8, 369–378. 3. Thayer, J.P. Rayleigh lidar system for middle atmosphere research in the arctic. Opt. Eng. 1997, 36, 2045–2061. [CrossRef] 4. Carswell, A.I.; Pal, S.R.; Steinbrecht, W.; Whiteway, J.A.; Ulitsky, A.; Wang, T.Y. Lidar measurements of the middle atmosphere. Can. J. Phys. 1991, 69, 1076–1086. [CrossRef] 5. Nishizawa, T.; Jin, Y.; Sugimoto, N.; Sato, K.; Okamoto, H. Observation of clouds, aerosols, and precipitation by multiple-field-of- view multiple-scattering polarization lidar at 355 nm. J. Quant. Spectrosc. Radiat. Transf. 2021, 271, 107710. [CrossRef] 6. Ninomiya, H.; Yaeshima, S.; Ichikawa, K.; Fukuchi, T. Raman lidar system for hydrogen gas detection. Opt. Eng. 2007, 46, 094301. [CrossRef] 7. Choi, I.Y.; Baik, S.H.; Cha, J.H.; Kim, J.H. Hydrogen gas concentration measurement method using the raman lidar system. Meas. Sci. Technol. 2019, 30, 055201. [CrossRef] 8. Zeyn, J.; Lahmann, W.; Weitkamp, C. Remote daytime measurements of tropospheric temperature profiles with a rotational raman lidar. Opt. Lett. 1996, 21, 1301–1303. [CrossRef] 9. Chust, G.; Galparsoro, I.; Ángel, B.; Franco, J.; Uriarte, A. Coastal and estuarine habitat mapping, using lidar height and intensity and multi-spectral imagery. Estuar. Coast. Shelf Sci. 2008, 78, 633–643. [CrossRef] 10. Lin, Y.; Hyyppa, J.; Jaakkola, A. Mini-uav-borne lidar for fine-scale mapping. IEEE Geosci. Remote Sens. Lett. 2011, 8, 426–430. [CrossRef] 11. Fisher, C.T.; Cohen, A.S.; Fernández-Diaz, J.C.; Leisz, S.J. The application of airborne mapping lidar for the documentation of ancient cities and regions in tropical regions. Quatern. Int. 2017, 448, 129–138. [CrossRef] 12. Koyama, M.; Shiina, T. Light source module for led mini-lidar. Rev. Laser Eng. 2011, 39, 617–621. [CrossRef] 13. Shiina, T. LED mini lidar for atmospheric application. Sensors 2019, 19, 569. [CrossRef] 14. Rocadenbosch, F.; Soriano, C.; Comerón, A.; Baldasano, J.M. Lidar inversion of atmospheric backscatter and extinction-to- backscatter ratios by use of a Kalman filter. Appl. Opt. 1999, 38, 3175–3189. [CrossRef] 15. Zhou, Z.; Hua, D.; Wang, Y.; Yan, Q.; Li, S.; Yan, L.; Wang, H. Improvement of the signal to noise ratio of Lidar echo signal based on wavelet de-noising technique. Opt. Laser Eng. 2013, 51, 961–966. [CrossRef] 16. Yang, G.; Liu, Y.; Wang, Y.; Zhu, Z. EMD interval thresholding denoising based on similarity measure to select relevant modes. Signal Process. 2015, 109, 95–109. [CrossRef] 17. Yan, S.; Yang, G.; Li, Q.; Wang, C. Waveform centroid discrimination of pulsed Lidar by combining EMD and intensity weighted method under low SNR conditions. Infrared Phys. Technol. 2020, 109, 103385. [CrossRef] 18. Dragomiretskiy, K.; Zosso, D. Variational mode decomposition. IEEE Trans. Signal Process. 2013, 62, 531–544. [CrossRef] 19. Li, J.; Zhang, X.; Tang, J. Noise suppression for magnetotelluric using variational mode decomposition and detrended fluctuation analysis. J. Appl. Geophys. 2020, 180, 104127. [CrossRef] 20. Liu, Z.; Chang, J.; Li, H.; Chen, S. Signal denoising method combined with variational mode decomposition, machine learning online optimization and the interval thresholding technique. IEEE Access 2020, 8, 223482–223494. [CrossRef] 21. Diao, X.; Jiang, J.; Shen, G.; Chi, Z.; Wang, Z.; Ni, L.; Mebarki, A.; Bian, H.; Hao, Y. An improved variational mode decomposition method based on particle swarm optimization for leak detection of liquid pipelines. Mech. Syst. Signal Pract. 2020, 143, 106787. [CrossRef] 22. Garg, H. A hybrid PSO-GA algorithm for constrained optimization problems. Appl. Math. Comput. 2016, 274, 292–305. [CrossRef] Information 2022, 13, 558 14 of 14 23. Behnam, M.; Pourghassem, H. Spectral correlation power-based seizure detection using statistical multi-level dimensionality reduction and PSO-PNN optimization algorithm. IETE J. Res. 2017, 63, 736–753. [CrossRef] 24. Eloranta, E.E. High Spectral Resolution Lidar. In Springer Series in Optical Sciences; Georgia Institute of Technology: Atlanta, GA, USA, 2005; Volume 102, pp. 143–163. 25. Kunz, G.J.; Leeuw, G. Inversion of lidar signals with the slope method. Appl. Opt. 1993, 32, 3249–3256. [CrossRef] [PubMed] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Information Multidisciplinary Digital Publishing Institute

LED-Lidar Echo Denoising Based on Adaptive PSO-VMD

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Abstract

information Article 1 1 2 1 1 3 , Ziqi Peng , Hongzi Bai , Tatsuo Shiina , Jianglong Deng , Bei Liu and Xian Zhang * College of Mathematics and Physics, Hunan University of Arts and Science, Changde 415000, China Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan School of Geosciences and Info-Physics, Central South University, Changsha 410083, China * Correspondence: [email protected]; Tel.: +86-731-8887-2258 Abstract: LED (light-emitting diode)-lidar (light detection and ranging) has gradually been focused on by researchers because of its characteristics of low power, high stability, and safety to human eyes. However, LED-lidar systems are easily disturbed by background light noise. Echo signal denoising is an essential work that directly affects the measurement accuracy of the LED-lidar system. The traditional variational modal decomposition (VMD) method in lidar signal denoising relies on practical experience to optimize the critical parameters of quadratic penalty factor and the number of intrinsic mode function (IMF) components K globally, which is hard to denoise effectively. For this problem, a denoising method based on VMD with the adaptive weighted particle swarm optimization (PSO) is proposed in this work. The PSO-VMD method adaptively adjusts the weight value ! for different lidar echo signals and optimizes of the parameters and K globally. The LED-lidar echo signals are denoised by moving average, VMD, and PSO-VMD. Using the denoised echo signals, the range compensation waveforms and the extinction coefficients are derived. The results show that the PSO-VMD denoised echo signal has the highest R-square value of 0.9972 and the minimum standard deviation value of 5.7369, while the values of r-square and standard deviation of the echo signal denoised by moving average and VMD method are 0.9902, 9.7450, 0.9945, and 7.3588, respectively. The derived distance compensation waveforms and extinction coefficients based on the PSO-VMD denoising have better stability than those based on the moving average and VMD denoising. Citation: Peng, Z.; Bai, H.; Shiina, T.; Keywords: LED-lidar; denoising; variational modal decomposition; particle swarm optimization Deng, J.; Liu, B.; Zhang, X. LED-Lidar Echo Denoising Based on Adaptive PSO-VMD. Information 2022, 13, 558. https://doi.org/10.3390/info13120558 1. Introduction Academic Editor: Zahir M. Hussain As a typical optical remote sensing technology [1], lidar (light detection and rang- ing) is widely applied in environmental monitoring, geographic mapping, hazardous gas Received: 25 July 2022 detection, and other applications [2–11]. With the development of industrialization and Accepted: 26 November 2022 the increasingly severe global environmental problems, the environmental monitoring Published: 29 November 2022 applications of lidar, especially atmospheric aerosol monitoring, have been widely studied Publisher’s Note: MDPI stays neutral by researchers. Compared with chemical sensor measurement techniques, lidar has the with regard to jurisdictional claims in advantages of a wide measurement range, high accuracy, and the ability to obtain the published maps and institutional affil- spatial distribution of the aerosol by scanning. These advantages benefit from the collima- iations. tion and high-power characteristics of the laser light source. However, the high-quality laser is expensive, bulky, has a high power consumption, and is strict for the use of the environment. More importantly, the use of high-power lasers in the central part of the city, urban buildings, and densely populated spaces has safety risks to human eyes. These Copyright: © 2022 by the authors. factors make lidar mainly used in developed countries or advanced regions, and its use Licensee MDPI, Basel, Switzerland. environment is limited in laboratories and sparsely populated areas. Lidar is challenging to This article is an open access article be applied in densely populated areas of cities for various types of monitoring applications. distributed under the terms and The safety of the light source, the compactness of the lidar device, and the power conditions of the Creative Commons consumption are essential factors in close- and small-range aerosol monitoring applications, Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ such as dust monitoring on factory floors, exhaust gas emission monitoring in factories, 4.0/). flammable and explosive gas monitoring in hydrogen energy station, etc. For these reasons, Information 2022, 13, 558. https://doi.org/10.3390/info13120558 https://www.mdpi.com/journal/information Information 2022, 13, 558 2 of 14 this study focuses on the lidar system with LED (light-emitting diode) as the light source. Although LED is inferior to laser in terms of collimation, emission power, and spectral line width, it has many advantages that lasers do not have: low price, low energy consumption, low-voltage working power, high stability, high applicability, high flexibility in application, and safety to human eyes. For these advantages, LED is widely applied in various scenarios. The Shiina’s group from Chiba University started the application of LED-lidar ear- lier. Several prototypes such as in-line-type and dual-axis-type LED-lidar were created by their team [12,13]. Their team applied the LED-lidar system in surface atmospheric measurements and successfully acquired close-range atmospheric echo signals. However, the LED light source is difficult to collimate, and its radiated power decreases rapidly with increasing distance, which makes the LED-lidar system vulnerable to the influence of background light noise. It is challenging to meet the high-precision measurement in spatial resolution and dynamic range. To improve the applicability of LED-lidar in various applications, echo signal denoising is vital work. However, the difference in power and collimation between LED-lidar and traditional lidar makes the dynamic range of LED-lidar echo signal much smaller than that of traditional lidar. The simple denoising method, such as moving average, cannot remove the noise of LED-lidar echo well, even wrongly removing the LED-lidar echo signal as background noise. Therefore, an effective denoising method can improve the accuracy of aerosol monitoring with LED-lidar, especially in long distances with a low value of signal-to-noise ratio (SNR). The lidar echo is a nonlinear and nonstationary signal. Nonlinear denoising algorithms such as Kalman filter (KF), wavelet transform (WT), empirical mode decomposition (EMD), and other algorithms have been applied in the application of lidar denoising. KF is a recur- sive algorithm based on minimum mean square error, which can process nonstationary and multidimensional signals from time-varying systems. However, the calculation accuracy of this method decreases significantly when the signals change dramatically [14]. WT can decompose signals into different frequency components through multiscale analysis, which has good localization characteristics in the time–frequency domain. However, it has poor adaptability due to the selection of the wavelet basis function [15]. EMD made up for the inadequacy of WT, which has good adaptability and can reflect the characteristics of the specific frequency of the signal. However, it has the endpoint effect and modal aliasing problems due to the recursive mode decomposition characteristics of the EMD method, which hinders the separation of the echo signal from noise [16,17]. For these reasons, variational mode decomposition (VMD) is proposed to solve the problem above. VMD can effectively avoid the problems of modal aliasing and endpoint effect caused by EMD. However, it is found that the quadratic penalty factor a and the number of intrinsic mode function (IMF) components K have a significant influence on its decomposition effect [18]. The traditional VMD method combines the local optimal solution of and K by experimental method and empirical method, respectively [19]. However, the combination of local optimal solutions is challenging to achieve the global optimal effect because of the correlation between and K parameters. To increase the denoising effect of VMD in LED-lidar applications, an algorithm that can optimize critical parameter combinations [ , K] is needed [20]. Particle swarm optimization (PSO) is an intelligent algorithm with global optimization ability [21]. The algorithm finds the optimal solution through cooperation and information sharing among individuals in a group. It has been widely used in function optimization, neural network training, fuzzy system control, and other applications of genetic algorithms due to its simple operation and fast convergence [22,23]. However, for traditional PSO, it is difficult to achieve local optimization and global optimization synchronously because the weight parameter ! is set as a constant. It can obtain a better global optimization effect if the ! can be assigned dynamically in different original signals. In this paper, the parameters [ , K] of VMD are optimized by the PSO algorithm with adaptive weights, and the VMD is used to denoise the LED-lidar echo signals. To estimate the effectiveness of the PSO-VMD algorithm, the same LED-lidar atmospheric Information 2022, 13, 558 3 of 14 echo signals are denoised with the moving average method, the VMD algorithm, and the PSO-VMD algorithm, respectively, and the denoised results are compared. The improved effect of denoising from the PSO-VMD is also estimated from the calculation result of the extinction coefficient. The main content of this paper is as follows: Section 1 presents the background of LED- lidar and the algorithm of lidar signal denoising. Section 2 offers the PSO-VMD method. Section 3 introduces the LED-lidar system, data acquisition, and calculation process of extinction coefficient. Section 4 presents the results of LED-lidar signal denoising with PSO-VMD and the other methods. Section 5 is the conclusion. 2. Theory 2.1. VMD VMD is a new multicomponent signal decomposition algorithm based on Wiener filtering, Hilbert transform, and outlier demodulation [18]. VMD can decompose a signal f (t) into K discrete modes m (k = 1, 2, 3 , K). m are amplitude–frequency modulated k k (AM-FM) signals, and their bandwidths have sparsity in the frequency domain, effectively suppressing the modal aliasing that occurs in EMD. Each m is compacted around the center frequency, and its bandwidth can be obtained by Gaussian smoothing demodulation. The constrained variational problem in the VMD can be expressed as: 8 8 99 < < h  i == jw t 2 min ¶ d(t) + m (t) e å k 2 pt : : ;; fm g,fw g k k k (1) S.t. m (t) = f fm g = fm , m  m g and fw g = fw , w w g are the sets of the decomposed 2 2 k 1 K k 1 K modes and their central frequencies, respectively. The quadratic penalty parameter a and the Lagrange multiplier operator l(t) are introduced to obtain the solution to the constrained variational problem in Equation (1). The augmented Lagrangian function is expressed as: h  i jw t 2 L m , w , l = a ¶ d(t) +  m (t) e (f g f g ) k k t k pt 2 (2) + f (t) m .(t) + l(t), f (t) m (t) å k å k k k The saddle point of Equation (2) can be obtained by the alternating direction method of multipliers. Then m , w , and l can be updated iteratively in the frequency domain. k k The steps of VMD are as follows: 1 1 1 (a) Initializing m , w , l and setting n = 0; k k (b) Updating m and w iteratively by Equations (3) and (4), respectively: k k l(w) f (w) m (w) + i6=k n+1 2 m (w) = (3) 1 + 2a(w w ) ¥ 2 wjm (w)j dw n+1 0 w = R (4) k ¥ jm (w)j dw (c) Updating l according to Equation (5): 2 3 n+1 n n+1 4 5 l (w) l (w) + t f (w) m (w) (5) k Information 2022, 13, 558 4 of 14 (d) Repeating steps (b)–(c) until the iteration result is satisfied the ending condition: n+1 n 2 n 2 km m k /km k < # (6) å k 2 k 2 where # is the discriminant accuracy, and # > 0. (e) Outputting K modal components. 2.2. PSO PSO is an algorithm for global optimization of key parameters, and determination of the fitness function is a key step in the PSO algorithm [21]. The fitness function is updated with the change in particle position, and the updated direction of the particle is dependent on the value of the fitness function. The minimum of the envelope entropy is used as the fitness function, which represents the sparsity of the original signal. The envelope entropy is more prominent when the signal-to-noise power ratio is small. On the other hand, the envelope entropy value is smaller when the signal-to-noise power ratio is significant. The envelope entropy E can be expressed as: E = p lg p (7) p å j j j=1 a(j) p = (8) j=1 2 2 a(j) = x (j) + x (j) (9) where p is the sequence of probability distributions of a(j); a(j) is the envelope obtained from the Hilbert demodulation of x(j). The weight parameter ! in the traditional PSO algorithm is set as a constant, which easily leads to the problem of local optima. An adaptive nonlinear dynamic inertial weight coefficient !, as shown in Equation (10), was adopted in the PSO algorithm to optimize the VMD parameters in this study. The flowchart of the adaptive-weight PSO-VMD is shown in Figure 1. The nonlinear dynamic inertial weight is closely related to the global optima, which can vary with the position of particles, and solve the problem of local optima. (w w ) f f max ( avg) min w , f  f avg min f f avg w = min (10) w , f > f max avg where f is the fitness function, which is E mentioned in Equation (7); f is the average of p avg the fitness function; and f is the minimum of the fitness function. min The calculation steps of PSO-VMD are as follows: (a) Parameter initialization: the main parameters are the population size, the maximum number of iterations, and the search range of the parameters and K. (b) Updating iteratively: using the minimum of envelope entropy as the fitness function and updating the velocity and position of the population iteratively. (c) Determining the adaptive nonlinear dynamic inertial weight ! according to the most calculated current envelope entropy and the mean value of envelope entropy. (d) Update the new optimal [ , K] and the minimum envelope entropy if the new calcu- lated envelope entropy is smaller than the minimum of the envelope entropy. (e) Repeat steps (b)–(d) until the maximum number of iterations as well as the minimum envelope entropy is determined; output the optimal parameters and K. Information Information2022 2022 ,,13 13 ,, x FOR PEER 558 REVIEW 5 of 5 of 14 14 Figure 1. Flowchart of the adaptive-weight particle swarm optimization (PSO) - variational modal Figure 1. Flowchart of the adaptive-weight particle swarm optimization (PSO) - variational modal decomposition (VMD). decomposition (VMD). 3. LED-Lidar System and Signal Processing The calculation steps of PSO-VMD are as follows: 3.1. LED-Lidar System (a) Parameter initialization: the main parameters are the population size, the maximum A biaxial type of LED-lidar was used in this study [13]. Figure 2 shows the schematic number of iterations, and the search range of the parameters α and K. diagram of LED-lidar and its prototype used in this study. The LED pulse driver provides (b) Updating iteratively: using the minimum of envelope entropy as the fitness function a pulse with a high frequency of 500 kHz and a pulse width of 10 ns, which is used to and updating the velocity and position of the population iteratively. drive a high-power LED with a wavelength of 395 nm. The LED has an average power of (c) Determining the adaptive nonlinear dynamic inertial weight ω according to the most 3.82 mW and a peak power of 764 mW. The beam from LED is collimated by a combination calculated current envelope entropy and the mean value of envelope entropy. of a silicone lens and a Fresnel lens and emitted from the transmitter with a diffusion angle (d) Update the new optimal [α, K] and the minimum envelope entropy if the new calcu- of 12.5 mrad. The transmitted beam generates the backscattering light while propagating lated envelope entropy is smaller than the minimum of the envelope entropy. in the aerosol. The backscattering light is focused by the telescope and collimating lens. (e) Repeat steps (b)–(d) until the maximum number of iterations as well as the minimum After filtering with a special filter and bandpass filter, the focused light is converted to envelope entropy is determined; output the optimal parameters α and K. electrical signals by a photomultiplier tube (PMT). The photon counter is used for the integral operation to make the LED-lidar echo signal stable. The LED-lidar echo samples 3. LED-Lidar System and Signal Processing used in this study are obtained from the photon counter with 10 integrals. 3.1. LED-Lidar System A biaxial type of LED-lidar was used in this study [13]. Figure 2 shows the schematic diagram of LED-lidar and its prototype used in this study. The LED pulse driver provides a pulse with a high frequency of 500 kHz and a pulse width of 10 ns, which is used to drive a high-power LED with a wavelength of 395 nm. The LED has an average power of 3.82 mW and a peak power of 764 mW. The beam from LED is collimated by a combina- tion of a silicone lens and a Fresnel lens and emitted from the transmitter with a diffusion angle of 12.5 mrad. The transmitted beam generates the backscattering light while propa- gating in the aerosol. The backscattering light is focused by the telescope and collimating Information 2022, 13, x FOR PEER REVIEW 6 of 14 lens. After filtering with a special filter and bandpass filter, the focused light is converted to electrical signals by a photomultiplier tube (PMT). The photon counter is used for the Information 2022, 13, 558 6 of 14 integral operation to make the LED-lidar echo signal stable. The LED-lidar echo samples used in this study are obtained from the photon counter with 10 integrals. (a) (b) Figure 2. LED-lidar system: (a) schematic diagram; (b) prototype. Figure 2. LED-lidar system: (a) schematic diagram; (b) prototype. 3.2. Lidar Echo Signal and Signal Processing 3.2. Lidar Echo Signal and Signal Processing The analysis of LED-lidar echo signal is based on the lidar equation [24]: The analysis of LED-lidar echo signal is based on the lidar equation [24]: 𝑐𝜏 1 ct 1 (11) 𝑃 𝑟 =𝑃 ∙𝐾 ∙𝑌 𝑟 ∙ 𝐴 ∙ ∙𝛽 𝑟 ∙ ∙exp 2𝜎𝑟 P(r) = P KY(r) A  b(r)  exp(2sr) (11) 2 𝑟 2 r where 𝑟 is the measurement distance; 𝑃 𝑟 is the received power; 𝑃 is the transmitted where r is the measurement distance; P(r) is the received power; P is the transmitted power; 𝐾 is the system efficiency determined by the optical system of LED-lidar; 𝑌 is the power; K is the system efficiency determined by the optical system of LED-lidar; Y is the geometric overlap coefficient, representing the overlap rate of the field of view between geometric overlap coefficient, representing the overlap rate of the field of view between receiver and transmitter, which is determined by the angle of view of transmitter and re- receiver and transmitter, which is determined by the angle of view of transmitter and ceiver; 𝐴 is the receiving area of the receiver determined by the aperture of the telescope; receiver; A is the receiving area of the receiver determined by the aperture of the telescope; 𝑐 is the speed of light; 𝜏 is the pulse width of light; 𝛽 is the atmospheric backscattering c is the speed of light; t is the pulse width of light; b is the atmospheric backscattering coefficient; and 𝜎 is atmospheric extinction coefficient. coefficient; and s is atmospheric extinction coefficient. Figure 3 shows the backscattering echo signals from atmospheric aerosols obtained Figure 3 shows the backscattering echo signals from atmospheric aerosols obtained by by LED-lidar. The x-axis is the distance derived from the flight time of the photon. The y- LED-lidar. The x-axis is the distance derived from the flight time of the photon. The y-axis axis is the intensity of the LED-lidar echo signal with the unit of count. At a distance of is the intensity of the LED-lidar echo signal with the unit of count. At a distance of about about 17 m, the geometric overlap coefficient of the system approaches 1, and the echo 17 m, the geometric overlap coefficient of the system approaches 1, and the echo signal of signal of atmospheric aerosol decreases exponentially with the increase in distance. As the atmospheric aerosol decreases exponentially with the increase in distance. As the geometric overlap coefficient increases gradually from 0 in the near distance, the backscattering echo shows an increasing trend in the close space. The maximum signal in the waveform is the point where the field overlap rate of the transmitter and receiver reaches the top. The geometric overlap coefficient reaches the top. Only the part of the signal farther than the Information 2022, 13, 558 7 of 14 maximum point can effectively evaluate the optical properties of atmospheric aerosol. The echo signal contains harmonic noise carried from the pulse modulation process. Due to the short pulse width of 10 ns and the precision of the modulation circuit, it is easy to form unstable harmonics, which become a part of the echo noise after being amplified by the LED driver. The background light is another kind of echo noise. Especially for the echo with low intensity obtained from a far distance, it is more susceptible to the influence of background light. 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 50 100 150 200 250 300 Distance (m) Figure 3. A typical backscattering echo signals from atmospheric aerosols. Atmospheric extinction coefficient s is an important parameter used to evaluate the optical characteristics of atmospheric aerosol. Although the atmospheric extinction coeffi- cient has a spatial distribution, it is difficult to find the reference of the spatial distribution of the extinction coefficient on the surface to evaluate the denoising effect. Therefore, the average atmospheric extinction coefficient within a period of time is used as a reference to evaluate the denoising effect. The most classical slope method [25] is adopted to derive the parameter s. The deriving process of s is as follows: (a) Carrying out the product operation of r for both sides of the lidar equation. (b) Taking the natural logarithm for both sides of the equation. (c) Taking the derivative of r for both sides of the equation. As the parameters P , K, Y(r), A , c, and t are constant, the new equation can be 0 r written as: d ln P(r)r 1 db(r) =  2s (12) dr b(r) dr Considering that the atmosphere is homogeneous, and the backscattering coefficient b is a constant, then db(r)/dr = 0. The homogeneous atmospheric extinction coefficient can be expressed in the following form: d ln P(r)r s (r) =  (13) 2 dr According to Equation (12), compensating the echo signal by multiplication of r , and taking the natural logarithm, the extinction coefficient can be derived as 1/2 of the slope of the compensated waveform, which is formed by the function of ln P(r)r . Lidar echo (count) Information 2022, 13, x FOR PEER REVIEW 8 of 14 Information 2022, 13, 558 8 of 14 Figure 4 shows the waveform of the LED-lidar echo after range compensation. Due Figure 4 shows the waveform of the LED-lidar echo after range compensation. Due to the low signal intensity of the long-range echo, the compensated echo signal is easily to the low signal intensity of the long-range echo, the compensated echo signal is easily affected by the background light noise. After the range compensation, the background affected by the background light noise. After the range compensation, the background light light noise at the long range is further amplified, making the signal at the long range un- noise at the long range is further amplified, making the signal at the long range unstable. stable. The slope of the middle and rear waveform is calculated as the extinction coeffi- The slope of the middle and rear waveform is calculated as the extinction coefficient. The cient. The red dashed line is a linear fitted line obtained from the part of the range com- red dashed line is a linear fitted line obtained from the part of the range compensation signal, pensation signal, which is further than 100 m, and 1/2 of its slope is the extinction coeffi- which is further than 100 m, and 1/2 of its slope is the extinction coefficient characterized cient characterized by the LED-lidar. The instability of the signal at the long range is prone by the LED-lidar. The instability of the signal at the long range is prone to error in the to error in the process of the linear fit, especially when batch processing large amounts of process of the linear fit, especially when batch processing large amounts of LED-lidar echo LED-lidar echo data. Therefore, for the high-accuracy linear fit of the range compensation data. Therefore, for the high-accuracy linear fit of the range compensation signal, effective signal, effective LED-lidar echo denoising is an indispensable work in this study. LED-lidar echo denoising is an indispensable work in this study. 15.8 linear fitted (red dashed line) 15.6 15.4 15.2 14.8 14.6 14.4 14.2 0 50 100 150 200 250 300 Distance (m) Figure 4. Figure 4.LED- LED-lidar lidar eecho cho wave waveform form after range compensation. after range compensation. 4. Result 4. Result 4.1. Denoising of LED-Lidar Echo 4.1. Denoising of LED-Lidar Echo The moving average, VMD, and PSO-VMD are used to denoise the atmospheric aerosol The moving average, VMD, and PSO-VMD are used to denoise the atmospheric aer- echo signals of the LED-lidar. The denoising results are shown in Figure 5. Figure 5a–c osol echo signals of the LED-lidar. The denoising results are shown in Figure 5. Figure 5a– shows the denoising results using moving average, VMD, and PSO-VMD, respectively, and c show the denoising results using moving average, VMD, and PSO-VMD, respectively, the details of the waveform in the interval from 100 m to 300 m are shown in the box on and the details of the waveform in the interval from 100 m to 300 m are shown in the box the right side of the figure. Figure 5d shows the comparison of the denoising effect of the on the right side of the figure. Figure 5d shows the comparison of the denoising effect of three methods. In Figure 5a, the result of the denoised echo is based on the 5-point moving the three methods. In Figure 5a, the result of the denoised echo is based on the 5-point average, which shows that the moving average method can effectively suppress the noise moving average, which shows that the moving average method can effectively suppress and make the echo signal smooth partly. The longer the moving average length, the better the noise and make the echo signal smooth partly. The longer the moving average length, the noise suppression effect. However, the information is easily lost if the average length is the better the noise suppression effect. However, the information is easily lost if the aver- set as a large value. Due to the steep gradient of signal intensity in the peak region, part age length is set as a large value. Due to the steep gradient of signal intensity in the peak of the information in the peak region is lost after moving average denoising, which is the region, part of the information in the peak region is lost after moving average denoising, disadvantage of the moving average method. Figure 5b shows the denoising results of the which is the disadvantage of the moving average method. Figure 5b shows the denoising VMD with the empirical parameters [ = 200, K = 5]. The selection of parameters [ , K] results of the VMD with the empirical parameters [α = 200, K = 5]. The selection of param- is crucial in VMD denoising. For the same set of data, different parameter selection can eters [α, K] is crucial in VMD denoising. For the same set of data, different parameter achieve other denoising effects. Similarly, for the same set of empirical parameters [ , K], selection can achieve other denoising effects. Similarly, for the same set of empirical pa- different denoising effects can be obtained when processing other data. Compared with rameters [α, K], different denoising effects can be obtained when processing other data. the moving average method, the VMD method not only overcomes the disadvantage of the C information ompared wloss ith the m brought oviby ng av theer moving age meaverage thod, the method VMD m due ethod no to a long t onl moving y overco average mes the but disadvantage of the information loss brought by the moving average method due to a also better suppresses the signal fluctuations in the region of low intensity. Figure 5c shows long mov the denoising ing ar vesults erage but based also bet on PSO-VMD. ter suppresse As the s the sign initialization al flucof tua PSO, tions in the the article region swarm of low sizeint is e set nsias ty.10, Figur maximum e 5c shows iterations the deno number ising res isu set lts as based 10, on and PS minimum O-VMD. As fitness the in value itialiis - set as 0.001. Thanks to the parameter optimization of PSO, the denoised echo signal not zation of PSO, the article swarm size is set as 10, maximum iterations number is set as 10, only maintains the same intensity level as the original echo signal but also finely rejects the ln( p(r) * r )(a.u.) Information 2022, 13, x FOR PEER REVIEW 9 of 14 and minimum fitness value is set as 0.001. Thanks to the parameter optimization of PSO, Information 2022, 13, 558 9 of 14 the denoised echo signal not only maintains the same intensity level as the original echo signal but also finely rejects the subtle noise. The denoised echo signal is smoother than the one obtained by the empirical parameters of VMD. Figure 5d shows the comparison subtle noise. The denoised echo signal is smoother than the one obtained by the empirical of the three methods of denoising results in the region of 100–300 m. The moving average parameters of VMD. Figure 5d shows the comparison of the three methods of denoising denoising not only has information loss but also cannot suppress the signal fluctuation results in the region of 100–300 m. The moving average denoising not only has information caused by the noise. The PSO-VMD has the best performance in signal denoising and fluc- loss but also cannot suppress the signal fluctuation caused by the noise. The PSO-VMD has tuation suppressing. the best performance in signal denoising and fluctuation suppressing. 10,000 10,000 Original lidar echo Original lidar echo 9000 9000 Moving average denoising VMD denoising 8000 8000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Distance (m) Distance (m) (a) (b) 10,000 450 Moving average denoising Original lidar echo VMD denoising PSO-VMD denoising 390 PSO-VMD denoising 0 30 0 50 100 150 200 250 300 100 140 180 220 260 300 Distance (m) Distance (m) (c) (d) Figure 5. Denoising result of LED-lidar echo: (a) moving average; (b) VMD; (c) PSO-VMD; (d) com- Figure 5. Denoising result of LED-lidar echo: (a) moving average; (b) VMD; (c) PSO-VMD; parison of (a–c). (d) comparison of (a–c). In the measurement of atmospheric aerosols, the ideal lidar echo should be close to In the measurement of atmospheric aerosols, the ideal lidar echo should be close to the exponential attenuation when the distribution of aerosols is uniform, and the geomet- the exponential attenuation when the distribution of aerosols is uniform, and the geometric ric overlap coefficient of the lidar system is 1. Fifty samples are selected from the denoising overlap coefficient of the lidar system is 1. Fifty samples are selected from the denoising signals obtained by the three different methods and the original echo signal, respectively. signals obtained by the three different methods and the original echo signal, respectively. The 100–300 m range of the signal was selected and fitted exponentially. The average R- The 100–300 m range of the signal was selected and fitted exponentially. The average square and root mean squared error (RMSE) were calculated. The calculation results are R-square and root mean squared error (RMSE) were calculated. The calculation results are shown in Table 1 The R-square represents the similarity between the experimental signal shown in Table 1 The R-square represents the similarity between the experimental signal and the ideal fitted signal. The closer the value is to 1, the closer the experimental signal and the ideal fitted signal. The closer the value is to 1, the closer the experimental signal is to the ideal fitted signal. Compared with the original echo signal before denoising, the is to the ideal fitted signal. Compared with the original echo signal before denoising, the R- R-squar square va e values lues of of the deno the denoised ised sisignals gnals ar ar e sign e significantly ificantly improved, e improved, s especially pecially for for th the e PSO- PSO- VMD denoising, the R-square value reaches the highest value of 0.9972. RMSE re VMD denoising, the R-square value reaches the highest value of 0.9972. RMSE repr presents esents the the dev deviation iation bbetween etween th the e eexperimental xperimental ssignal ignal an and d the the ide ideal al fi fitted tted si signal. gnal. The sm The smaller aller th the e value is, th value is, the e closer closer the expe the experimental rimental sign signal al is to the is to the idea ideal l fitted s fitted igna signal. l. Com Compar pared with ed with the the original signal before denoising, the RMSE of the signal after denoising decreased original signal before denoising, the RMSE of the signal after denoising decreased signif- significantly, especially the RMSE of the PSO-VMD denoising result, which reaches the icantly, especially the RMSE of the PSO-VMD denoising result, which reaches the mini- minimum value of 5.7369. Although the optimization parameters based on experience were mum value of 5.7369. Although the optimization parameters based on experience were used in VMD denoising, due to the difference between signals caused by the random error of measurement environment and background light, it is difficult to achieve the optimal denoising of all data with the optimization parameters based on experience. Comparing Lidar echo (count) Lidar echo (count) Lidar echo (count) Lidar echo (count) Information 2022, 13, x FOR PEER REVIEW 10 of 14 used in VMD denoising, due to the difference between signals caused by the random error of measurement environment and background light, it is difficult to achieve the optimal denoising of all data with the optimization parameters based on experience. Comparing the R-Square and RMSE values of VMD and PSO-VMD, it shows that PSO has a significant optimization effect on VMD in LED-lidar denoising. Information 2022, 13, 558 10 of 14 Table 1. Comparison of R-square and RMSE with the three denoising methods. Denoising Method R-Square RMSE the R-Square and RMSE values of VMD and PSO-VMD, it shows that PSO has a significant Original echo 0.9421 24.0928 optimization effect on VMD in LED-lidar denoising. Moving average 0.9902 9.7450 VMD 0.9945 7.3588 Table 1. Comparison of R-square and RMSE with the three denoising methods. PSO-VMD 0.9972 5.7369 Denoising Method R-Square RMSE Original echo 0.9421 24.0928 4.2. Range Compensation Moving average 0.9902 9.7450 VMD 0.9945 7.3588 As mentioned in Section 3.2, before solving the extinction coefficient of the LED-lidar PSO-VMD 0.9972 5.7369 aerosol echo signal with the slope method, the range compensation is required. However, as the distance increases, the compensated value to the echo signal gradually increases, 4.2. Range Compensation and the noise is also amplified by the multiplication of range compensation. The signal- As mentioned in Section 3.2, before solving the extinction coefficient of the LED-lidar to-noise ratio of the distant echo signal is smaller than that of the near echo signal, which aerosol echo signal with the slope method, the range compensation is required. However, leads to increasing fluctuations in the range compensation as the distance increases. The as the distance increases, the compensated value to the echo signal gradually increases, fluctuation and the of the r noise is a also nge ampli compensation b fied by the multiplication rings a significant error of range compensation. to calculating The signal- the slope by to-noise ratio of the distant echo signal is smaller than that of the near echo signal, which a linear fit. The range compensation was carried out after denoising the original echo sig- leads to increasing fluctuations in the range compensation as the distance increases. The nal of LED-lidar by moving average, VMD, and PSO-VMD, respectively. The calculation fluctuation of the range compensation brings a significant error to calculating the slope results are shown in Figure 6. Figure 6a–c show the range compensation results by using by a linear fit. The range compensation was carried out after denoising the original echo the denoised signal to deal with the moving average method, VMD, and PSO-VMD, re- signal of LED-lidar by moving average, VMD, and PSO-VMD, respectively. The calculation spectively. Comparing the range compensation results of the echo signal after denoising results are shown in Figure 6. Figure 6a–c show the range compensation results by using by the the th denoised ree methods signal wi totdeal h that with of th the e origin moving alaverage signal, method, the fluctu VMD, ation of and the d PSO-VMD, istant signal respectively. Comparing the range compensation results of the echo signal after denoising is suppressed. The denoising process removes part of the noise in the distant signal with by the three methods with that of the original signal, the fluctuation of the distant signal low SNR, which reduces the noise amplification from the range compensation. Figure 6d is suppressed. The denoising process removes part of the noise in the distant signal with compares the range compensation results denoised by the three methods. Compared with low SNR, which reduces the noise amplification from the range compensation. Figure 6d the moving average method, the range compensation result of VMD denoising has some compares the range compensation results denoised by the three methods. Compared improvement in suppressing fluctuation. However, the effect is not apparent, since IMF with the moving average method, the range compensation result of VMD denoising has some improvement in suppressing fluctuation. However, the effect is not apparent, since components K determined empirically is not the optimal value. On the other hand, com- IMF components K determined empirically is not the optimal value. On the other hand, pared with the VMD denoising, the PSO-VMD denoised range compensated signal is sig- compared with the VMD denoising, the PSO-VMD denoised range compensated signal nificantly improved in signal fluctuation. The high-frequency components from back- is significantly improved in signal fluctuation. The high-frequency components from ground noise and white noise are also suppressed, which is the effect of the critical pa- background noise and white noise are also suppressed, which is the effect of the critical rameters of K and α optimized by the PSO. parameters of K and optimized by the PSO. 16 16 Range compensation without denoising Range compensation without denoising 15.8 15.8 Moving average range compensation VMD range compensation 15.6 15.6 15.4 15.4 15.2 15.2 14.8 14.8 14.6 14.6 14.4 14.4 14.2 14.2 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Distance (m) Distance (m) (a) (b) Figure 6. Cont. ln( p(r) * r ) (a.u.) ln( p(r) * r ) (a.u.) Information 2022, 13, x FOR PEER REVIEW 11 of 14 Information 2022, 13, 558 11 of 14 16 15.6 Moving average range compensation Range compensation without denoising 15.8 VMD range compensation PSO-VMD range compensation 15.5 PSO-VMD range compensation 15.6 15.4 15.4 15.2 15 15.3 14.8 15.2 14.6 14.4 15.1 14.2 14 15 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Distance (m) Distance (m) (c) (d) Figure 6. LED-lidar echo range compensation: (a) moving average; (b) VMD; (c) PSO-VMD; (d) Figure 6. LED-lidar echo range compensation: (a) moving average; (b) VMD; (c) PSO-VMD; comparison of (a–c). (d) comparison of (a–c). 4.3. Extinction Coefficient 4.3. Extinction Coefficient A set of LED-lidar echoes containing 196 samples was denoised with moving average, A set of LED-lidar echoes containing 196 samples was denoised with moving aver- VMD, and PSO-VMD, and the extinction coefficients at different time points were derived. age, VMD, and PSO-VMD, and the extinction coefficients at different time points were The samples were acquired on the night of 26 March 2019 (cloudy) in the city of Changde. derived The. The LED-lidar sample was s wer set on e ac the quired 6th floor on of the nigh the second t of laboratory 26 March building 2019 (cloud of the y) Hunan in the city of University of Arts and Sciences, with an elevation angle of 60 . The period of sample Changde. The LED-lidar was set on the 6th floor of the second laboratory building of the acquisition was from 19:27 to 21:24. The number of data integration times was set as 10 Hunan University of Arts and Sciences, with an elevation angle of 60°. The period of sam- (mentioned in Section 3.1), and the acquisition time of each sample was about 40 s. ple acquisition was from 19:27 to 21:24. The number of data integration times was set as Figure 7 shows the extinction coefficients derived from the data in the region of 10 (mentioned in Section 3.1), and the acquisition time of each sample was about 40 s. 100–300 m, which was denoised by the moving average, VMD, and PSO-VMD. For all Figure 7 shows the extinction coefficients derived from the data in the region of 100– the samples, the PSO initialization was set as the parameters mentioned in Section 4.1. The x-axis is the time point, and the y-axis is the extinction coefficient. Although the 300 m, which was denoised by the moving average, VMD, and PSO-VMD. For all the calculation region and the elevation angle of LED-lidar were set as constant, the extinction samples, the PSO initialization was set as the parameters mentioned in Section 4.1. The x- coefficients derived by three methods fluctuated by varying degrees. The instability of the axis is the time point, and the y-axis is the extinction coefficient. Although the calculation extinction coefficient is influenced by the flow of surface–atmosphere and variations of region and the elevation angle of LED-lidar were set as constant, the extinction coefficients surface urban environmental conditions. On the other hand, the nonlinear signal itself, the derived by three methods fluctuated by varying degrees. The instability of the extinction influence of noise, and the poor adaptability of the fitting algorithm are also the reasons coefficient is influenced by the flow of surface–atmosphere and variations of surface ur- causing the extinction coefficients to fluctuate. According to Lambert Beer ’s law, the extinction coefficient, in theory, should be negative values because of the light scattering ban environmental conditions. On the other hand, the nonlinear signal itself, the influence in the atmosphere when light propagates in the atmosphere. However, some extinction of noise, and the poor adaptability of the fitting algorithm are also the reasons causing the coefficients with positive values were still obtained in this study. Due to the intense extinction coefficients to fluctuate. According to Lambert Beer’s law, the extinction coeffi- background light appearing in some data samples, even the excellent PSO-VMD method cient, in theory, should be negative values because of the light scattering in the atmos- could not remove the noise at a long distance, which leads to the fact that as the noise is phere when light propagates in the atmosphere. However, some extinction coefficients amplified in the process of range compensation, the range compensated signal intensity with positive values were still obtained in this study. Due to the intense background light at a long distance is higher than that at a short distance. The slope of the linear fitting becomes a positive value. Compared with the derived extinction coefficients by moving appearing in some data samples, even the excellent PSO-VMD method could not remove average and VMD method, the number of positive values of extinction coefficients derived the noise at a long distance, which leads to the fact that as the noise is amplified in the by the PSO-VMD method is only 4, which is the least. The result indicates that the PSO- process of range compensation, the range compensated signal intensity at a long distance VMD method can remove the noise from background light more effectively. The standard is higher than that at a short distance. The slope of the linear fitting becomes a positive deviations of the extinction coefficients derived by moving average, VMD, and PSO-VMD 4 4 4 value. Compared with the derived extinction coefficients by moving average and VMD were calculated, and the values were 5.7452  10 , 4.7309  10 , and 2.2896  10 , method, respectively the nu.m Due ber o to f the posuperiorit sitive valu y of esPSO-VMD of extinction denoising, coefficien the fluctuation ts derived b of y extinction the PSO-VMD coefficients obtained by PSO-VMD is minimal. method is only 4, which is the least. The result indicates that the PSO-VMD method can remove the noise from background light more effectively. The standard deviations of the extinction coefficients derived by moving average, VMD, and PSO-VMD were calculated, −4 −4 −4 and the values were 5.7452 × 10 , 4.7309 × 10 , and 2.2896 × 10 , respectively. Due to the superiority of PSO-VMD denoising, the fluctuation of extinction coefficients obtained by PSO-VMD is minimal. ln( p(r) * r ) (a.u.) ln( p(r) * r ) (a.u.) Information 2022, 13, x FOR PEER REVIEW 12 of 14 Information 2022, 13, 558 12 of 14 2.0E-3 -3 2.0×10 By Moving Average By VMD By PSO-VMD -3 1.0×10 1.0E-3 -3 0.0×10 0.0E+0 -3 -1 -1 .0 .0× E10 -3 -2.0E-3 -3 -2.0×10 -3 -3.0×10 -3.0E-3 19:27 19:42 19:56 20:11 20:25 20:39 20:54 21:08 21:23 Time (mm:ss) Figure 7. Figure 7.The The eextinction xtinction co coef efficients of atmo ficients of atmospheric spheric ae aer rosol osolderived by thre derived by three e d denoising enoising method methods. s. To evaluate the accuracy of the extinction coefficients derived from the LED-lidar echo, To evaluate the accuracy of the extinction coefficients derived from the LED-lidar the extinction coefficients were derived from the surface visibility released by the Hunan echo, the extinction coefficients were derived from the surface visibility released by the provincial meteorological department and compared with the average values of the three Hunan provincial meteorological department and compared with the average values of sets of extinction coefficients calculated from LED-lidar echo. The conversion formula from the three sets of extinction coefficients calculated from LED-lidar echo. The conversion visibility to extinction coefficient is expressed as Equation (14): formula from visibility to extinction coefficient is expressed as Equation (14): 3.912 3.912 550 550 s =  (1 (14) 4) 𝜎= ∙ n 𝜈 l𝜆 where 𝜎 is the extinction coefficient, 𝜈 is the visibility, and 𝜆 is the wavelength of the where s is the extinction coefficient, n is the visibility, and l is the wavelength of the light light source. The visibility on March 26 was about 10 km, and the wavelength of the light source. The visibility on March 26 was about 10 km, and the wavelength of the light source source was 395 nm. According to the parameters of visibility and wavelength, the extinc- was 395 nm. According to the parameters of visibility and wavelength, the extinction coeffi- −4 −1 4 1 tion coefficient was calculated as 5.6 × 10 m . The mean values of extinction coefficients cient was calculated as 5.6  10 m . The mean values of extinction coefficients derived 4 1 −4 −1 4 −1 4 derived by moving average, VMD, and PSO-VMD were 6.7609 × 10 m , 6.4250 × 10 by moving average, VMD, and PSO-VMD were 6.7609  10 m , 6.4250  10 m , −1 4 −41−1 m , 5.7401 × 10 m , respectively. The average value of the extinction coefficient derived 5.7401  10 m , respectively. The average value of the extinction coefficient derived by by PSO-VMD is closest to the value of the extinction coefficient derived from visibility, PSO-VMD is closest to the value of the extinction coefficient derived from visibility, which which indicates the superiority of PSO-VMD in extinction coefficient calculation. indicates the superiority of PSO-VMD in extinction coefficient calculation. 5. Conclusions 5. Conclusions For the characteristics of nonlinear, low SNR, and low dynamic range in LED-lidar echo For the characteristics of nonlinear, low SNR, and low dynamic range in LED-lidar signal, a novel denoising method based on VMD with adaptive-weight PSO is proposed. echo signal, a novel denoising method based on VMD with adaptive-weight PSO is pro- Compared with the traditional VMD denoising method, this method dynamically assigns posed. Compared with the traditional VMD denoising method, this method dynamically the weights w in the PSO algorithm for the different echo signals. It globally optimizes the assigns the weights 𝜔 in the PSO algorithm for the different echo signals. It globally op- critical parameters [ , K] of VMD, which further improves the denoising effect. timizes the critical parameters [α, K] of VMD, which further improves the denoising effect. Echo signal denoising, range compensation, and extinction coefficient calculation were Echo signal denoising, range compensation, and extinction coefficient calculation performed by using moving average, VMD, and PSO-VMD, respectively. The denoised were performed by using moving average, VMD, and PSO-VMD, respectively. The de- echo signal based on PSO-VMD has the optimal R-square value of 0.9972 and the minimum noised echo signal based on PSO-VMD has the optimal R-square value of 0.9972 and the RMSE value of 5.7369. In the calculation of range compensation, the result based on PSO- minimum RMSE value of 5.7369. In the calculation of range compensation, the result VMD denoising has the slightest fluctuation at long distance. In the analysis of extinction based on PSO-VMD denoising has the slightest fluctuation at long distance. In the analysis coefficient, the extinction coefficients based on PSO-VMD denoising have the best stability. of extinction coefficient, the extinction coefficients based on PSO-VMD denoising have the Under the condition of intense background light and incomplete denoising, the number best stability. Under the condition of intense background light and incomplete denoising, of error points of slope fitting with PSO-VMD denoising is the least. The superiority of the number of error points of slope fitting with PSO-VMD denoising is the least. The su- PSO-VMD in LED-lidar denoising is proved by analysis of the three critical signals. periority of PSO-VMD in LED-lidar denoising is proved by analysis of the three critical However, a constant region and parameters were used in the calculation of linear signals. fitting, resulting in a small number of slope fitting error points when the SNR of the echo However, a constant region and parameters were used in the calculation of linear signal is low and the fluctuation is significant. In the future, the introduction of machine fitting, resulting in a small number of slope fitting error points when the SNR of the echo signal is low and the fluctuation is significant. In the future, the introduction of machine −1 Extinction Coefficient (m ) Information 2022, 13, 558 13 of 14 learning is considered, which can better perform adaptive linear fitting to further reduce the fluctuation of extinction coefficient. Author Contributions: Conceptualization, Z.P.; methodology, Z.P. and B.L.; software, B.L., X.Z. and H.B.; validation, Z.P., T.S. and J.D.; formal analysis, Z.P. and T.S.; investigation, Z.P. and H.B.; resources, X.Z.; data curation, Z.P. and B.L. writing—original draft preparation, Z.P.; writing—review and editing, Z.P.; visualization, Z.P. and T.S.; supervision, T.S.; project administration, Z.P.; funding acquisition, Z.P. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the Natural Science Youth Foundation of Hunan Province (2020JJ5396), Excellent Young Scientist Foundation of Hunan Provincial Education Department (20B405), and the Research Foundation for Advanced Talents (18BSQD32). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not Applicable, the study does not report any data. Conflicts of Interest: The authors declare no conflict of interest. References 1. Jaboyedoff, M.; Oppikofer, T.; Abellán, A.; Derron, M.; Loye, A.; Metzger, R.; Pedrazzini, A. Use of lidar in landslide investigations: A review. Nat. Hazards 2012, 61, 5–28. [CrossRef] 2. Qiu, J.; Lu, D. On lidar application for remote sensing of the atmosphere. Adv. Atmos. Sci. 1991, 8, 369–378. 3. Thayer, J.P. Rayleigh lidar system for middle atmosphere research in the arctic. Opt. Eng. 1997, 36, 2045–2061. [CrossRef] 4. Carswell, A.I.; Pal, S.R.; Steinbrecht, W.; Whiteway, J.A.; Ulitsky, A.; Wang, T.Y. Lidar measurements of the middle atmosphere. Can. J. Phys. 1991, 69, 1076–1086. [CrossRef] 5. Nishizawa, T.; Jin, Y.; Sugimoto, N.; Sato, K.; Okamoto, H. Observation of clouds, aerosols, and precipitation by multiple-field-of- view multiple-scattering polarization lidar at 355 nm. J. Quant. Spectrosc. Radiat. Transf. 2021, 271, 107710. [CrossRef] 6. Ninomiya, H.; Yaeshima, S.; Ichikawa, K.; Fukuchi, T. Raman lidar system for hydrogen gas detection. Opt. Eng. 2007, 46, 094301. [CrossRef] 7. Choi, I.Y.; Baik, S.H.; Cha, J.H.; Kim, J.H. Hydrogen gas concentration measurement method using the raman lidar system. Meas. Sci. Technol. 2019, 30, 055201. [CrossRef] 8. Zeyn, J.; Lahmann, W.; Weitkamp, C. Remote daytime measurements of tropospheric temperature profiles with a rotational raman lidar. Opt. Lett. 1996, 21, 1301–1303. [CrossRef] 9. Chust, G.; Galparsoro, I.; Ángel, B.; Franco, J.; Uriarte, A. Coastal and estuarine habitat mapping, using lidar height and intensity and multi-spectral imagery. Estuar. Coast. Shelf Sci. 2008, 78, 633–643. [CrossRef] 10. Lin, Y.; Hyyppa, J.; Jaakkola, A. Mini-uav-borne lidar for fine-scale mapping. IEEE Geosci. Remote Sens. Lett. 2011, 8, 426–430. [CrossRef] 11. Fisher, C.T.; Cohen, A.S.; Fernández-Diaz, J.C.; Leisz, S.J. The application of airborne mapping lidar for the documentation of ancient cities and regions in tropical regions. Quatern. Int. 2017, 448, 129–138. [CrossRef] 12. Koyama, M.; Shiina, T. Light source module for led mini-lidar. Rev. Laser Eng. 2011, 39, 617–621. [CrossRef] 13. Shiina, T. LED mini lidar for atmospheric application. Sensors 2019, 19, 569. [CrossRef] 14. Rocadenbosch, F.; Soriano, C.; Comerón, A.; Baldasano, J.M. Lidar inversion of atmospheric backscatter and extinction-to- backscatter ratios by use of a Kalman filter. Appl. Opt. 1999, 38, 3175–3189. [CrossRef] 15. Zhou, Z.; Hua, D.; Wang, Y.; Yan, Q.; Li, S.; Yan, L.; Wang, H. Improvement of the signal to noise ratio of Lidar echo signal based on wavelet de-noising technique. Opt. Laser Eng. 2013, 51, 961–966. [CrossRef] 16. Yang, G.; Liu, Y.; Wang, Y.; Zhu, Z. EMD interval thresholding denoising based on similarity measure to select relevant modes. Signal Process. 2015, 109, 95–109. [CrossRef] 17. Yan, S.; Yang, G.; Li, Q.; Wang, C. Waveform centroid discrimination of pulsed Lidar by combining EMD and intensity weighted method under low SNR conditions. Infrared Phys. Technol. 2020, 109, 103385. [CrossRef] 18. Dragomiretskiy, K.; Zosso, D. Variational mode decomposition. IEEE Trans. Signal Process. 2013, 62, 531–544. [CrossRef] 19. Li, J.; Zhang, X.; Tang, J. Noise suppression for magnetotelluric using variational mode decomposition and detrended fluctuation analysis. J. Appl. Geophys. 2020, 180, 104127. [CrossRef] 20. Liu, Z.; Chang, J.; Li, H.; Chen, S. Signal denoising method combined with variational mode decomposition, machine learning online optimization and the interval thresholding technique. IEEE Access 2020, 8, 223482–223494. [CrossRef] 21. Diao, X.; Jiang, J.; Shen, G.; Chi, Z.; Wang, Z.; Ni, L.; Mebarki, A.; Bian, H.; Hao, Y. An improved variational mode decomposition method based on particle swarm optimization for leak detection of liquid pipelines. Mech. Syst. Signal Pract. 2020, 143, 106787. [CrossRef] 22. Garg, H. A hybrid PSO-GA algorithm for constrained optimization problems. Appl. Math. Comput. 2016, 274, 292–305. [CrossRef] Information 2022, 13, 558 14 of 14 23. Behnam, M.; Pourghassem, H. Spectral correlation power-based seizure detection using statistical multi-level dimensionality reduction and PSO-PNN optimization algorithm. IETE J. Res. 2017, 63, 736–753. [CrossRef] 24. Eloranta, E.E. High Spectral Resolution Lidar. In Springer Series in Optical Sciences; Georgia Institute of Technology: Atlanta, GA, USA, 2005; Volume 102, pp. 143–163. 25. Kunz, G.J.; Leeuw, G. Inversion of lidar signals with the slope method. Appl. Opt. 1993, 32, 3249–3256. [CrossRef] [PubMed]

Journal

Information – Multidisciplinary Digital Publishing Institute

Published: Nov 29, 2022

Keywords: LED-lidar; denoising; variational modal decomposition; particle swarm optimization

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