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

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