Lidar is a powerful tool for detecting atmospheric temperature, humidity, and aerosols. The lidar echo signal forms the basis for retrieving these parameters. Currently, data acquisition cards with fixed sampling rates are widely used to sample lidar echo signals. However, the bandwidth of the lidar echo signal is much larger than the sampling rate of the acquisition card, which inevitably leads to distortion of the signal. In addition, high-speed data sampling consumes substantial resources for data acquisition, storage, and processing, which is particularly problematic in space-borne lidar systems. With the development of digital signal processing technologies, compressed sensing has found widespread application in data compression, noise reduction, and other fields. We aim to reconstruct the lidar echo signal precisely with fewer sampling points using compressed sensing.

In this paper, compressed sensing theory is used to reconstruct the lidar echo signal with fewer sampling points. First, the sparsity of the lidar echo signal is analyzed using the db4 wavelet base. Then, based on the wavelet basis and the orthogonal matching pursuit (OMP) algorithm, the downsampling and compressed reconstruction of the lidar echo signal are investigated under different noise conditions. The error between the reconstructed and original lidar echo signals is analyzed in detail. Finally, the extinction coefficient of aerosols below 10 km is retrieved using the reconstructed lidar echo signal through the Fernald method, and the error between the retrieved extinction coefficient and the standard atmosphere model is analyzed. The validity of the reconstructed lidar echo signal for data retrieval is confirmed.

In the wavelet decomposition, three decomposition layers are used, with 0.01% of the maximum value of the wavelet coefficient set as the threshold. The research results show that most of the wavelet decomposition coefficients are close to zero, which indicates the sparsity of the lidar echo signal in the wavelet basis (Fig. 3). When the lidar detection height is 10 km, the total number of decomposition coefficients is 10020, with 1238 non-zero coefficients after thresholding. Using these non-zero coefficients, the lidar echo signal is reconstructed through inverse wavelet transform. The similarity of the reconstructed lidar echo signal is as high as 0.999, and the root-mean-square error is 8.666×10^-17, further confirming the high sparsity of the lidar echo signal in the wavelet basis (Fig. 4). Based on the high sparsity of the lidar echo signal, downsampling and compressed reconstruction are performed under different noise conditions. The results show that the lidar echo signal can be reconstructed using fewer sampling points through compressed sensing. The signal-to-noise ratio (SNR) and the similarity of the reconstructed signal improve as the SNR of the input signal increases. When the data compression ratio is 5∶1 and the input signal’s SNR exceeds 25 dB, the similarity between the reconstructed and original signals is greater than 0.997 (Table 3). The SNR of the reconstructed signal is higher than that of the input signal, indicating that the OMP algorithm has a certain denoising effect (Fig. 8). Finally, the extinction coefficient of aerosols below 10 km is retrieved using the reconstructed lidar echo signal through the Fernald method. The lidar echo signal is reconstructed from the input signal, with an SNR of 30 dB. The profile of the extinction coefficient is consistent with the standard atmosphere model. The relative error of the retrieved extinction coefficient at different heights is below 15.81%, confirming the validity of the reconstructed lidar echo signal for retrieving aerosol extinction coefficients (Fig. 11).

First, the high sparsity of the ground-based lidar echo signal is confirmed. The results show that when the detection distance is 10 km, the sparsity of the lidar echo signal in the wavelet basis is only 1238. Second, the lidar echo signal can be accurately reconstructed using the orthogonal matching pursuit algorithm. The SNR of the input signal significantly affects the reconstruction quality. When the data compression ratio is 5∶1 and the SNR of the input signal exceeds 25 dB, the similarity between the reconstructed and original signals exceeds 0.997, and the root-mean-square error is less than 1.769×10^-13. Finally, the extinction coefficient of aerosols below 10 km is retrieved using the reconstructed lidar echo signal through the Fernald method. When the input signal’s SNR is 30 dB, the absolute error in the retrieved aerosol extinction coefficient is less than 2.440×10^-7 m^-1, and the relative error is less than 15.81%, which verifies the effectiveness of the reconstructed signal for retrieving aerosol extinction coefficients.