Improved waveform decomposition with bound constraints for green waveforms of airborne LiDAR bathymetry

Abstract. Waveform decomposition using the Levenberg–Marquardt algorithm is a powerful tool for detecting surface return, bottom return, and volume backscatter return in a superposed green waveform of airborne LiDAR bathymetry (ALB). However, traditional decomposition methods do not handle bound constraints and are easily trapped in local optimum. Thus, the decomposed components may be inconsistent with the measurement principle of ALB. This study proposes an improved waveform decomposition method by setting reasonable lower and upper bounds of waveform parameters to guarantee the fidelity of the decomposed components. First, a comprehensive mathematical model of a green waveform is proposed by considering the early return. Second, the lower and upper bounds of the waveform parameters are given on the basis of the measurement principle of ALB. Finally, improved waveform decomposition is achieved using the comprehensive model and a constrained nonlinear optimization. The proposed method is applied to a practical ALB measurement using Optech coastal zone mapping and imaging LiDAR. Compared with traditional decomposition methods, the improved waveform decomposition not only ensures good fitness but also guarantees the fidelity of the decomposed components.