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

TL;DR

This paper introduces a Bayesian model and algorithm for depth and intensity profiling from sparse, low-photon-count Lidar waveforms, leveraging hierarchical modeling and MCMC for improved accuracy.

Contribution

It proposes a novel Bayesian hierarchical model with MRF priors and an adaptive MCMC algorithm for analyzing low-photon-count Lidar data.

Findings

Effective depth and intensity estimation from sparse data

Automatic parameter tuning via maximum marginal likelihood

Validated with real-world experiments

Abstract

This paper presents a new Bayesian model and algorithm used for depth and intensity profiling using full waveforms from the time-correlated single photon counting (TCSPC) measurement in the limit of very low photon counts. The model proposed represents each Lidar waveform as a combination of a known impulse response, weighted by the target intensity, and an unknown constant background, corrupted by Poisson noise. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters and their constraints. In particular, a gamma Markov random field (MRF) is used to model the joint distribution of the target intensity, and a second MRF is used to model the distribution of the target depth, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to compute the Bayesian estimates of interest and perform Bayesian inference. 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 serie of experiments using real data.