BB-spline deconvolution for differential target cross-section determination in full-waveform laser scanning data

In full-waveform laser scanning, short laser pulses are emitted and travel towards Earth and object surfaces. The sensor samples the waveform of the emitted pulse and its complete backscattered echo as a function of time. This technique allows for the three-dimensional reconstruction of the terrain, natural and man-made objects, and for the derivation of (geo-)physical quantities such as the differential target cross-section. The retrieval of the differential target cross-section requires deconvolution which is an ill-posed problem. In this study, we present a novel technique for the computation of the differential target cross-section using BB-splines. This class of mathematical functions enables a well-posed linear approach for deconvolution. Furthermore, it is not dependent on the symmetry of the temporal profiles of the emitted laser waveform and the received echoes, as approaches previously suggested. In this paper, the algorithm for deconvolution is presented in detail and validated for both synthetic and real-world full-waveform laser scanner data.