Abstract
This paper presents two new algorithms for the joint restoration of depth and reflectivity (DR) images constructed from time-correlated single-photon counting measurements. Two extreme cases are considered: 1) a reduced acquisition time that leads to very low photon counts; and 2) imaging in a highly attenuating environment (such as a turbid medium), which makes the reflectivity estimation more difficult at increasing range. Adopting a Bayesian approach, the Poisson distributed observations are combined with prior distributions about the parameters of interest, to build the joint posterior distribution. More precisely, two Markov random field (MRF) priors enforcing spatial correlations are assigned to the DR images. Under some justified assumptions, the restoration problem (regularized likelihood) reduces to a convex formulation with respect to each of the parameters of interest. This problem is first solved using an adaptive Markov chain Monte Carlo (MCMC) algorithm that approximates the minimum mean square parameter estimators. This algorithm is fully automatic since it adjusts the parameters of the MRFs by maximum marginal likelihood estimation. However, the MCMC-based algorithm exhibits a relatively long computational time. The second algorithm deals with this issue and is based on a coordinate descent algorithm. Results on single-photon depth data from laboratory-based underwater measurements demonstrate the benefit of the proposed strategy that improves the quality of the estimated DR images.
Highlights
Reconstruction of 3-dimensional scenes is a challenging problem encountered in many applications
This paper introduced a hierarchical Bayesian model and two estimation algorithms for the restoration of depth and reflectivity obtained in the limit of very low photon counts and significant attenuation
A coordinate descent approach using an alternating direction method of multipliers algorithm was used to approximate the maximum a posteriori estimators. Both algorithms showed comparable performance while providing different characteristics, i.e., the Markov chain Monte Carlo (MCMC) algorithm was fully automatic while the coordinate descent algorithm (CDA) algorithm required a reduced computational time
Summary
Reconstruction of 3-dimensional scenes is a challenging problem encountered in many applications. The study focuses on the following two extreme cases: (i) a reduced data acquisition time and (ii) the use of an extremely attenuating medium [4] Both cases lead to a reduction in the number of detected photons per pixel, which affects the estimation of depth and target reflectivity. Taking underwater measurements leads to a severe attenuation of the intensity with respect to (w.r.t.) the target range, which makes the reflectivity estimation difficult With such challenging scenarios, the measurement can be improved by, for example, increasing the laser power or the data acquisition time [5], [6], this is not always practicable in a field situation.
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