Decomposition of LiDAR waveforms by B-spline-based modeling

Abstract Waveform decomposition is a widely used technique for extracting echoes from full-waveform LiDAR data. Most previous studies recommended the Gaussian decomposition approach, which employs the Gaussian function in laser pulse modeling. As the Gaussian-shape assumption is not always satisfied for real LiDAR waveforms, some other probability distributions (e.g., the lognormal distribution, the generalized normal distribution, and the Burr distribution) have also been introduced by researchers to fit sharply-peaked and/or heavy-tailed pulses. However, these models cannot be universally used, because they are only suitable for processing the LiDAR waveforms in particular shapes. In this paper, we present a new waveform decomposition algorithm based on the B-spline modeling technique. LiDAR waveforms are not assumed to have a priori shapes but rather are modeled by B-splines, and the shape of a received waveform is treated as the mixture of finite transmitted pulses after translation and scaling transformation. The performance of the new model was tested using two full-waveform data sets acquired by a Riegl LMS-Q680i laser scanner and an Optech Aquarius laser bathymeter, comparing with three classical waveform decomposition approaches: the Gaussian, generalized normal, and lognormal distribution-based models. The experimental results show that the B-spline model performed the best in terms of waveform fitting accuracy, while the generalized normal model yielded the worst performance in the two test data sets. Riegl waveforms have nearly Gaussian pulse shapes and were well fitted by the Gaussian mixture model, while the B-spline-based modeling algorithm produced a slightly better result by further reducing 6.4% of fitting residuals, largely benefiting from alleviating the adverse impact of the ringing effect. The pulse shapes of Optech waveforms, on the other hand, are noticeably right-skewed. The Gaussian modeling results deviated significantly from original signals, and the extracted echo parameters were clearly inaccurate and unreliable. The B-spline-based method performed significantly better than the Gaussian and lognormal models by reducing 45.5% and 11.5% of their fitting errors, respectively. Much more precise echo properties can accordingly be retrieved with a high probability. Benefiting from the flexibility of B-splines on fitting arbitrary curves, the new method has the potentiality for accurately modeling various full-waveform LiDAR data, whether they are nearly Gaussian or non-Gaussian in shape.