Lidar Waveform-Based Analysis of Depth Images Constructed Using Sparse Single-Photon Data

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.

Photon-efficient super-resolution laser radar

“…This is not a low number of photons per pixel comparable to recent works in which deconvolution is not needed, [14][15][16][17] but the results suggest that it is low enough that our explicit Poissonian modeling of observed photon counts improves performance. The flattened photon data cube f (Y) ∈ N nxny×nt is illustrated in image form in Fig.…”

“…Markov random field models, 14 and convex optimization. [15][16][17] One core assumption behind these existing lowlight depth imaging frameworks is that the spatial spot size of the illumination is small enough that we can assume that each pixel measurement has addressed a different scene patch.…”

Bayesian restoration of reflectivity and range profiles from subsampled single-photon multispectral Lidar data

“…According to [6], [14], each photon count y i,j, ,t is assumed to be drawn from the following Poisson distribution…”

“…However, a potential drawback of single photon counting is that the integration times required for accurate depth measurement can be too long for rapid depth profiling. Even with single-detector scanning systems, significant reductions in acquisition time have been demonstrated by application of advanced computational imaging approaches, such as first-photon imaging [5] or single-photon data analysis in the extremely photon-starved regime [6], [7], which have allowed depth images to be reconstructed with very few photon returns.…”

Computational single-photon depth imaging without transverse regularization

“…Very recently, computational imaging frameworks have been introduced to process photon detection data without treating a detection-time histogram as approximating a flux waveform, and using regularization predicated on piecewise smoothness in the transverse dimensions [6][7][8][9][10]. For natural scenes, accurate results have been demonstrated from as little as 1 detected photon per pixel, even in the presence of significant ambient light.…”