This paper presents a new Bayesian model and associated algorithm for depth
and intensity profiling using full waveforms from time-correlated single-photon
counting (TCSPC) measurements in the limit of very low photon counts (i.e.,
typically less than 20 photons per pixel). The model represents each Lidar
waveform as an unknown constant background level, which is combined in the
presence of a target, to a known impulse response weighted by the target
intensity and finally corrupted by Poisson noise. The joint target detection
and depth imaging problem is expressed as a pixel-wise model selection and
estimation problem which is solved using Bayesian inference. Prior knowledge
about the problem is embedded in a hierarchical model that describes the
dependence structure between the model parameters while accounting for their
constraints. In particular, Markov random fields (MRFs) are used to model the
joint distribution of the background levels and of the target presence labels,
which are both expected to exhibit significant spatial correlations. An
adaptive Markov chain Monte Carlo algorithm including reversible-jump updates
is then proposed to compute the Bayesian estimates of interest. This algorithm
is equipped with a stochastic optimization adaptation mechanism that
automatically adjusts the parameters of the MRFs by maximum marginal likelihood
estimation. Finally, the benefits of the proposed methodology are demonstrated
through a series of experiments using real data.Comment: arXiv admin note: text overlap with arXiv:1507.0251
