Bayesian Analysis of Lidar Signals with Multiple Returns

Time-correlated single photon counting and burst illumination laser data can be used for range profiling and target classification. In general, the problem is to analyze the response from a histogram of either photon counts or integrated intensities to assess the number, positions, and amplitudes of the reflected returns from object surfaces. The goal of our work is a complete characterization of the 3D surfaces viewed by the laser imaging system. The authors present a unified theory of pixel processing that is applicable to both approaches based on a Bayesian framework, which allows for careful and thorough treatment of all types of uncertainties associated with the data. We use reversible jump Markov chain Monte Carlo (RJMCMC) techniques to evaluate the posterior distribution of the parameters and to explore spaces with different dimensionality. Further, we use a delayed rejection step to allow the generated Markov chain to mix better through the use of different proposal distributions. The approach is demonstrated on simulated and real data, showing that the return parameters can be estimated to a high degree of accuracy. We also show some practical examples from both near and far-range depth imaging.