Scattering Suppression in Underwater LIDAR Signal Processing Based on Wavelet-ICA Method

A new underwater lidar signal-processing method based on wavelet transform (WT) and independent component analysis (ICA) is presented in this letter. The proposed method combines WT and ICA to overcome the drawbacks of ICA and WT applied independently. ICA requires the number of observations equal to or greater than the number of sources to be separated. In the new method, the observation matrix of ICA is constructed by multi-layer wavelet time-domain decomposition from a single measurement, which avoids the uncertainties in multiple measurements caused by the change of measurement conditions. In addition, the new method greatly improves the frequency resolution of the echo signal by introducing wavelet transform. It can remove both the low-frequency scattering and high-frequency electromagnetic noises in the obtained signals. The new approach was tested in an underwater lidar system. A pulsed 532 nm light source operates at a repetition rate of 50 kHz, with an average output power of 3 W and a pulse duration of less than 1 ns. An Avalanche Photo Diode (APD) detector and the acquisition system with a bandwidth of 1 GHz is used to receive the echo signals. Underwater target ranging experiments were conducted when the attenuation length (AL) was 10. The ranging accuracies were compared with different signal processing methods. When there was no scattering suppression algorithm applied, the ranging accuracy was 12 cm; with only ICA, the ranging accuracy was 6.8 cm, with only WT, the accuracy was 5 cm; using the Wavelet-ICA method, the ranging accuracy was improved to 2 cm. The signal processing method can suppress strong scattering clutter in turbid water, thus greatly improve the ranging accuracy.


Scattering Suppression in Underwater LIDAR
Signal Processing Based on Wavelet-ICA Method Xinyu Liu, Suhui Yang , Yangze Gao , Jing Li, Chaofeng Li, Zhen Xu, Xuetong Lin , and Chaoyang Fan Abstract-A new underwater lidar signal-processing method based on wavelet transform (WT) and independent component analysis (ICA) is presented in this letter.The proposed method combines WT and ICA to overcome the drawbacks of ICA and WT applied independently.ICA requires the number of observations equal to or greater than the number of sources to be separated.In the new method, the observation matrix of ICA is constructed by multi-layer wavelet time-domain decomposition from a single measurement, which avoids the uncertainties in multiple measurements caused by the change of measurement conditions.In addition, the new method greatly improves the frequency resolution of the echo signal by introducing wavelet transform.It can remove both the low-frequency scattering and high-frequency electromagnetic noises in the obtained signals.
The new approach was tested in an underwater lidar system.A pulsed 532 nm light source operates at a repetition rate of 50 kHz, with an average output power of 3 W and a pulse duration of less than 1 ns.An Avalanche Photo Diode (APD) detector and the acquisition system with a bandwidth of 1 GHz is used to receive the echo signals.Underwater target ranging experiments were conducted when the attenuation length (AL) was 10.The ranging accuracies were compared with different signal processing methods.When there was no scattering suppression algorithm applied, the ranging accuracy was 12 cm; with only ICA, the ranging accuracy was 6.8 cm, with only WT, the accuracy was 5 cm; using the Wavelet-ICA method, the ranging accuracy was improved to 2 cm.The signal processing method can suppress strong scattering clutter in turbid water, thus greatly improve the ranging accuracy.
Index Terms-Wavelet transform, independent component analysis, underwater target detection.

I. INTRODUCTION
T HE most pronounced advantages of lidar system over sonar system are higher spatial resolution and more flexible platform.However, due to the severe attenuation of laser beams in water, the detection distance of lidar is far inferior to that of sonar systems.The authors are with the School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China (e-mail: 3120205324@ bit.edu.cn;suhuiyang@bit.edu.cn;gao_yanze@bit.edu.cn;lijbrit@163.com;13978360015@163.com;3120215332@bit.edu.cn;316295883@bit.edu.cn;hello_fcy@163.com).
Color versions of one or more figures in this letter are available at https://doi.org/10.1109/LPT.2024.3357199.
Digital Object Identifier 10.1109/LPT.2024.3357199can be greatly reduced by using laser beam at wavelengths of 480 nm∼540 nm, which leaves overcoming scattering a greater challenge for underwater laser detection.The wavelet transform method (WT) introduces time and frequency scaling in its transformation, thereby achieving multi resolution analysis in time and frequency domains [1], [2].In recent years, people have introduced different types of wavelet processing methods [3], [4], [5], which were applied to optical filtering [6], [7], [8], and interference pattern analysis [9], [10].The wavelet transform method and traditional high-pass filtering utilize the spectral differences between the target echo and scattered clutters to separate the target and scattering.The wavelet transform method can improve the frequency resolution [11], thereby better distinguishing the target echo and scattered clutter in the echo frequency domain.Within the same passband, bandpass filtering (BP) will lose signals out of the passband.Contrarily, the wavelet transform method (WT) is an adaptive filtering algorithm, therefore, more echo signal was kept.However, in turbid water, the echo of underwater targets is often weak, and the spectrum of the scattering center contains high frequency components as well, with only high-pass filtering or WT, it is difficult to separate the target echo and scattered clutter.To solve this problem, we proposed the concept of introducing blind source separation into wavelet transform to achieve better separation of targets echo and scattering.
Blind source separation (BSS) can separate source signals from mixed observations without knowing the signals and the mixing parameters.Independent component analysis (ICA) [12], [13] is an important algorithm to realize BSS.It is based on the assumption that the mixed signals are statistically independent [14], [15].In underwater lidar system, the backward scattering clutters and target echoes are independent to each other [16], [17], therefore, ICA was applied to suppress backward scattering clutters and improve the ranging ability [18].In the ICA algorithm, the number of observations must equal or exceed the number of separated sources.Accordingly, to separate the target echo from backscattering clutter, we need more than two sets of detected signals as input to ICA.In cocktail problems, the input observations were attainted by different detector at the same time.In lidar scenario, the observations are achieved by multiple measurements under identical conditions.However, owing to the changes in water flow, the stability of the target, and the acquisition clock etc., it is difficult to realize that multiple measurements of  the same target is in the same state and condition.Changing of measurement condition will cause error of ICA algorithm.To solve this problem, we propose a single-measurement blind source separation algorithm based on wavelet transform (WT).
In this letter, a new signal processing algorithm which combines Wavelet transform (WT) and independent component analysis (ICA) is proposed in an underwater lidar system.The detected signals are decomposed into wavelet signals through multi-layer wavelet time-domain decomposition.The observation matrix in ICA is constructed with these wavelet signals and the original signal.Compared to multiple measurements, the new method only requires one set of echo signals to achieve blind source separation, avoiding the uncertainty of multiple measurements caused by changes in experimental conditions.Meanwhile, using the multi-layer wavelet timedomain decomposition as the observation matrix can greatly improve the frequency resolution of ICA.We compared the difference between WT-ICA and BP-ICA.The results also confirmed that WT-ICA is more efficient to suppress scattering clutters.

II. THEORETICAL PRINCIPLES
In order to solve the problem of the insufficient spectrum difference between scattering and target echo for WT, and multi-observation problem for ICA, we propose to combine ICA with wavelet transform.The method decomposes the original signal into several signals containing different spectrum information by wavelet transform, multiple data sets from WT decomposition are used as ICA observations.Fig. 1 shows the overall operation process of Wavelet-ICA.
In this method, we assume that the original echo signal is X (ω, t), ωdenotes frequency.The time domain decomposition results of signal X (ω, t) can be expressed as follows: Fig. 2 shows the overall operation process of multi-layer wavelet time-domain decomposition(Daubechies (dbn) wavelet basis function is used to reconstruct the underwater LiDAR echo signal).The method to decompose suppose X (ω, t) is the original signal, after first layer wavelet time-domain decomposition,X (ω, t)is decomposed to X (ω, t) ≈ X (ω 1 , t) + X ′ (ω 1 , t) in which, X ′ (ω 1 , t) is the high frequency component, and X (ω 1 , t) is the low frequency component.We repeat the procedure, always decompose the high frequency part of the previous decomposed wavelet, after nth decomposition, we obtain: the final result is expressed as: The spectrum range of the newly generated wavelet signal becomes half of the previous one, and its frequency resolution [19] is twice that of the previous one after each layer of decomposition.An observation matrix for ICA is constructed based on the results of multi-layer wavelet timedomain decomposition, which can be expressed as: where, X is an observation matrix constructed from the results of multi-layer wavelet time-domain decomposition, with each column composed of a set of wavelet signals.X is the input matrix of the Independent Component Analysis (ICA), which aims to obtain the source matrix from a given observation matrix.ICA separates the target signal from the scattering cluster according to the statistical independence between the signals.According to the central limit theorem [13], the aliased signal is the superposition of multiple independent components, which is more consistent with Gaussian distribution.The Gaussianity of aliased signal is stronger than that of the individual source signal.Therefore, non-Gaussianity is used as a standard to judge the independence of components to be separated.The length of the echo sequency is determined by the system acquisition rate.The more data is used, the more accurate of the algorithm is since the accuracy of the algorithm depends on the power density function (PDF) [20].In principle, increasing n can increase the accuracy of the algorithm, but due to the limited length of the data sequence, we found there is an optimal value of n, therefore, we take signal to clutter ratio (SCR) as a criteria, the optimal n corresponds to the highest SCR, in our experimental system, the optimum of n is 4.
III. RESULT Fig. 3 illustrates the experimental system.Light source was a Helios 532-3-50 pulsed laser (Coherent).The pulse duration was 1 ns, and the angle of divergence was 0.5 mrad.The light was incident on a mirror then reflected to the detection target surface in a 3 m water tank.The transmission through the mirror was received by a Photo Diode (PD) as the reference for ranging the underwater object.We used a black rubber pad as the target.The reflected signal was focused on an Avalanche Photo Diode (fluctuation range no more than 30 ps).We placed a 532 nm bandpass filter (5 nm full width at half maximum) in front of the Avalanche Photo Diode (APD) to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.filter out scattering noise in other bands.The field of view of the receiving optical system was 5 mrad, the receiving lens was 0.45 m away from the incident window of the water tank.
The distance from the mirror to the incident window of the water tank was 0.4 m, and the corresponding angle range of its incidence on different surfaces inside the water tank was 0∼3 • .The sampling rate of the data acquisition was 2.5 G per second.The time delay of the target was measured 100 times.The ranging accuracy is defined as the root mean square (RMS) value of measured distance which was calculated as 4.5 cm.The time delay of the laser beam in the underwater laser ranging system (fluctuation range no more than 50 ps) was 7.55∼7.73ns.The attenuation length (AL) was defined as the product of the propagating length of light in the medium and the attenuation coefficient of the medium.
The attenuation coefficient k was expressed as: where, x 1 and x 2 were the positions where the target was placed in the water, P 1 and P 2 were the reflected power measured by the power meter at the corresponding distances.Mg(OH) 2 were added into the water to change the attenuation coefficient k.We measured the attenuation coefficient ten times under same situation and used the average value.
To reduce the effect of water flow, in the experiment, we first added Mg(OH) 2 powders to the water, let the pump work for a period of time to ensure uniform mixing, and then we turned off the pump and did the ranging measurements.The attenuation coefficient was measured immediately after the ranging to ensure that the measured attenuation coefficient did not exceed the actual value.Fig. 4(a) demonstrates a  We set the target at 0.76 m, 1.08 m, 1.28 m, 1.55 m, 1.76 m and 2.00 m from the incident window of the water tank, respectively.Under different attenuation coefficients of water bodies, we applied the Wavelet-ICA, ICA, and WT methods to process the echo signals, and their respective processing results are shown in Fig. 5.
The pulse emission source's pulse duration was 1ns, and its corresponding distance was 11.25 cm.Therefore, we determined that the ranging error of the detected target was within 11 cm as an effective target.Under this measurement standard, we used peak detection method to determine flight time.With wavelet ICA method can detect up to 13 attenuation lengths.The application of the multi-layer wavelet timedomain decomposition method and ICA method can achieve target detection within 10 attenuation lengths; Without using any algorithm, only target in 8 attenuation lengths can be detected.In Fig. 6, at 10 attenuation lengths, without any scattering suppression algorithm, the ranging accuracy was 14 cm; When only ICA was used, the ranging accuracy was 6.8 cm.Similarly, with only WT, the ranging accuracy was 5 cm.The ranging accuracy had been improved to 2 cm using Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the Wavelet-ICA method.In Fig. 5, when the attenuation coefficient was constant, the ranging results gradually deteriorated with increasing distance.After applying Wavelet-ICA, ICA, and WT methods, the scattering effect was significantly reduced, and the ranging accuracy was significantly improved.The Wavelet-ICA, ICA, and WT methods had achieved similar results when the attenuation length is small.However, as the distance increases, the ranging results of the Wavelet-ICA method gradually outperform them.The results indicated that the separation ability of traditional ICA methods depends on the consistency among multiple measurement groups of the echo signal.In practical applications, achieving high consistency in multiple measurement groups of echo signals was difficult, so its separation ability was low.The Wavelet-ICA method only requires one set of echo signals and achieves multiple sets of echoes using multi-layer wavelet time-domain decomposition methods.The method used the results of multi-layer wavelet time-domain decomposition as the ICA observation matrix, significantly improving the dimension of the ICA observation matrix and thus enhancing its separation ability of the separation matrix.At the same time, this method used wavelet signals with higher frequency resolution as its observation matrix, thereby significantly improving the frequency resolution of the separation matrix.Similarly, the above results indicated that when the attenuation coefficient was constant, the target signal strength rapidly decreased with the increase in distance, and the influence of scattered clutter was significantly exacerbated.These factors result in a significant decrease in the spectral differentiation between the target and scattering, corresponding to an increase in the scattering components included in the bandwidth window of the wavelet basis function.The Wavelet-ICA method, in combination with ICA, can separate the scattering of this part, thereby reducing the scattering clutter impact compared to the former.

IV. CONCLUSION
A new signal-processing method for the underwater lidar system based on wavelet transform (WT) and independent component analysis (ICA) is presented in this letter.The signal processing method can suppress strong scattering clutter in turbid water, thus greatly improving the ranging accuracy.The experiment results showed that both the WT and Wavelet-ICA methods could improve the ranging accuracy of lidar in turbid water bodies.With Wavelet-ICA, the ranging accuracy was better than that with ICA or WT.The ranging error in a pulsed under water lidar system was reduced from 5 cm to less 2 cm at an AL of 10.The ranging method can enhance the underwater laser detection and ranging capability.

Fig. 5 .
Fig. 5.The measured distance by the lidar versus nominal distance when (a) k = 4.00 m −1 , (b) k = 5.00 m −1 , and (c) c = 6.00 m −1 .The waveform without the WT or ICA is represented by the black line.The red, blue, and pink curves respectively represent the results of ICA, WT, and Wavelet-ICA.

Fig. 6 .
Fig. 6.Ranging results and ranging errors of diffuse reflection target under different attenuation lengths.
The optical attenuation of water body includes absorption and scattering.The absorption

TABLE I RECEIVED
LASER POWERS AND THE CORRESPONDING ATTENUATION COEFFICIENTS OBTAINED AT SEVERAL POSITIONS