Comparison Analysis of Five Waveform Decomposition Algorithms for the Airborne LiDAR Echo Signal

The information from the components obtained by waveform decomposition is usually used to inverse topography, and classify tree species, etc. Many efforts on waveform decomposition algorithms have been presented, but they lack comparison analysis and evaluation. Thereby, this article compares and analyzes the performance of five waveform decomposition algorithms, which are Gaussian, Adaptive Gaussian, Weibull, Richardson–Lucy (RL), and Gold, under different topographic conditions such as forests, glaciers, lakes, and residential areas. The experimental results reveal that: first, the Gaussian algorithm causes the biggest fitting error at 9.96 mV in the forested area. It is easy to identify multiple dense peaks as single peaks. Second, there are many misjudged, superimposed, and overlapped waveform components separated by the Weibull algorithm. The Adaptive Gaussian is more capable of fitting complex waveforms but has 122 more outliers than the Weibull algorithm does. Third, the Gold and RL algorithms decompose the largest number of waveform components (272.2k and 265.9k) in the forested area; both RL and Gold algorithms can effectively improve the separability of peaks. Fourth, the RL algorithm is only more effective for the area with sparse vegetation than the Gold algorithm does, i.e., the Gold algorithm is capable of processing data with dense vegetation areas at a lowest false component detection rate of 1.3%, 0.9%, 1.1%, and 0.1% in four areas. Finally, the Gaussian and Gold algorithms have much faster decomposition speed at 1000/s and 2000/s than the other three algorithms do. These results are useful for selecting different algorithms under different environments.