Cross-section retrieval from full-waveform LiDAR using sparse solutions

Accurate waveform restoration, from the received noisy waveform, is of great interest to the full-waveform LiDAR community. As a result of this, important attributes could be estimated precisely which are valuable in describing and differentiating LiDAR targets. Assumptions behind prominent methods like the Gaussian decomposition do not hold due to the complexity of the land surface. Deconvolution is a standard approach to retrieve the target cross-section. A regularization method is proposed based on sparsity constraints and it is compared to other well-known deconvolution methods. Numerical and visual results illustrate the robustness of the proposed method with regard to signal restoration and to suppression of noise and oscillation effects.