This paper presents a new Bayesian model and associated algorithm
for depth and intensity profiling using full waveforms from timecorrelated
single-photon counting (TCSPC) measurements when the
photon count in very low. 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 problem which is solved using Bayesian
inference. A Reversible Jump Markov chain Monte Carlo algorithm
is proposed to compute the Bayesian estimates of interest. Finally,
the benefits of the methodology are demonstrated through a series of
experiments using real data.