Lidar waveform based analysis of depth images constructed using sparse\n single-photon data

Abstract

This paper presents a new Bayesian model and algorithm used for depth and\nintensity profiling using full waveforms from the time-correlated single photon\ncounting (TCSPC) measurement in the limit of very low photon counts. The model\nproposed represents each Lidar waveform as a combination of a known impulse\nresponse, weighted by the target intensity, and an unknown constant background,\ncorrupted by Poisson noise. Prior knowledge about the problem is embedded in a\nhierarchical model that describes the dependence structure between the model\nparameters and their constraints. In particular, a gamma Markov random field\n(MRF) is used to model the joint distribution of the target intensity, and a\nsecond MRF is used to model the distribution of the target depth, which are\nboth expected to exhibit significant spatial correlations. An adaptive Markov\nchain Monte Carlo algorithm is then proposed to compute the Bayesian estimates\nof interest and perform Bayesian inference. This algorithm is equipped with a\nstochastic optimization adaptation mechanism that automatically adjusts the\nparameters of the MRFs by maximum marginal likelihood estimation. Finally, the\nbenefits of the proposed methodology are demonstrated through a serie of\nexperiments using real data.\n