This paper presents a new Bayesian model and associated algorithm for depthand intensity profiling using full waveforms from time-correlated single-photoncounting (TCSPC) measurements in the limit of very low photon counts (i.e.,typically less than 20 photons per pixel). The model represents each Lidarwaveform as an unknown constant background level, which is combined in thepresence of a target, to a known impulse response weighted by the targetintensity and finally corrupted by Poisson noise. The joint target detectionand depth imaging problem is expressed as a pixel-wise model selection andestimation problem which is solved using Bayesian inference. Prior knowledgeabout the problem is embedded in a hierarchical model that describes thedependence structure between the model parameters while accounting for theirconstraints. In particular, Markov random fields (MRFs) are used to model thejoint distribution of the background levels and of the target presence labels,which are both expected to exhibit significant spatial correlations. Anadaptive Markov chain Monte Carlo algorithm including reversible-jump updatesis then proposed to compute the Bayesian estimates of interest. This algorithmis equipped with a stochastic optimization adaptation mechanism thatautomatically adjusts the parameters of the MRFs by maximum marginal likelihoodestimation. Finally, the benefits of the proposed methodology are demonstratedthrough a series of experiments using real data.
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