Gaussian Mixture Model with Variable Components for Full Waveform LiDAR Data Decomposition and RJMCMC Algorithm

Full waveform LiDAR data record the signal of the backscattered laser pulse. The elevation and the energy information of ground targets can be effectively obtained by decomposition of the full waveform LiDAR data. Therefore, waveform decomposition is the key to full waveform LiDAR data processing. However, in waveform decomposition, determining the number of the components is a focus and difficult problem. To this end, this paper presents a method which can automatically determine the number. First of all, a given full waveform LiDAR data is modeled on the assumption that energy recorded at elevation points satisfy Gaussian mixture distribution. The constraint function is defined to steer the model fitting the waveform. Correspondingly, a probability distribution based on the function is constructed by Gibbs. The Bayesian paradigm is followed to build waveform decomposition model. Then a RJMCMC (reversible jump Markov chain Monte Carlo) scheme is used to simulate the decomposition model, which determines the number of the components and decomposes the waveform into a group of Gaussian distributions. In the RJMCMC algorithm, the move types are designed, including updating parameter vector, splitting or merging Gaussian components, birth or death Gaussian component. The results obtained from the ICESat-GLAS waveform data of different areas show that the proposed algorithm is efficient and promising