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Accurate range determination and retrieval of the cross section are two important issues in the processing of full-waveform LiDAR\uddata, especially between closely located targets. The dependency of the received waveform on the emitted pulse can be removed\udthrough deconvolution and consequently comparisons between waveforms recorded by different sensors become feasible and\udmeaningful, since the cross-section is independent of system specifications. Common methods, such as the Wiener filter, are reported\udfor producing oscillation of the results around main peaks, along with negative values of the amplitude. Regularization is necessary\udto approximate a stable solution of deconvolution resistant to noise or error. A sparse solution of these linear inverse problems can\udbe attained by minimizing the one-norm of the solution. Satisfactory deconvolution results can then be achieved by utilizing sparsity\udconstraints. The results of regularization methods with sparse solutions have been evaluated using two synthetic datasets and\uddistinctions are highlighted for comparison with those from two widely used deconvolution methods, in terms of the level of surface\udresponse retrieval. The results presented indicate that the one-norm regularization approach can outperform the other methods\udconsidered

Sparsity based regularization approaches in reconstructing the range and cross section in full-waveform LiDAR