Abstract
This paper presents a new Bayesian model and algorithm used for depth and reflectivity profiling using full waveforms from the time-correlated single-photon counting measurement in the limit of very low photon counts. The proposed model represents each Lidar waveform as a combination of a known impulse response, weighted by the target reflectivity, and an unknown constant background, corrupted by Poisson noise. Prior knowledge about the problem is embedded through prior distributions that account for the different parameter constraints and their spatial correlation among the image pixels. In particular, a gamma Markov random field (MRF) is used to model the joint distribution of the target reflectivity, 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 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 series of experiments using real data.
Highlights
R ECONSTRUCTION of 3-dimensional scenes using timeof-flight light detection and ranging (Lidar) systems is a challenging problem encountered in many applications, including automotive [1]–[4], environment sciences [5], [6], architectural engineering and defence [7], [8]
For the measurements reported the optical path of the transceiver was configured to operate with a fiber-coupled illumination wavelength of 841nm, and a silicon single-photon avalanche diode (SPAD) detector
We proposed a new Bayesian model for Lidar-based low photon count imaging of single-layered targets
Summary
R ECONSTRUCTION of 3-dimensional scenes using timeof-flight light detection and ranging (Lidar) systems is a challenging problem encountered in many applications, including automotive [1]–[4], environment sciences [5], [6], architectural engineering and defence [7], [8]. The proposed method aims to estimate the respective contributions of the actual target and the background in the photon timing histograms It allows the estimation of the distance and reflectivity of the surface associated with each pixel, together with the average background levels, within a single estimation procedure. The main contributions of this work are 1) We develop new Bayesian reflectivity and depth models taking into account spatial correlations through Markovian dependencies These flexible models are embedded within the observation model for full waveform Lidarbased low photon count imaging 2) An adaptive Markov chain Monte Carlo algorithm is proposed to compute the Bayesian estimates of interest and perform Bayesian inference.
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