The combination of sparse sampling and image restoration can not only compress data capacity, but also improve imaging speed, which is of great significance for the development of high-resolution LiDAR imaging technology. In order to improve the restoration effect of sparse sampled images, a new residual channel attention network block was designed in the paper, and the residual channel attention block was introduced into a deep unfolding network based on compressed sensing iterative soft threshold method to suppress the blurring phenomenon caused by the loss of high-frequency information in image restoration and reconstruction, forming a new method for the restoration and reconstruction of sparse sampled LiDAR images. This method combines the advantages of traditional compressed sensing reconstruction methods and neural network methods, and has a faster reconstruction speed compared to traditional compressed sensing reconstruction methods. Compared with existing neural network methods, it enhances structural insight and improves the problem of image blur in reconstruction. The validation calculations using Middlebury Stereo Data 2006 as the test dataset show that our method not only has better image reconstruction quality compared to SDA, ReconNet, TVAL3, D-AMP, and IRCNN methods, but also has higher computational efficiency; When the sparse sampling ratio is 25%, the peak signal-to-noise ratio (PSNR) of the restored image is more than 1.6 dB higher than other methods, making it an ideal method for restoring sparse LiDAR images with good overall performance.