Computational multi-depth single-photon imaging

Abstract

We present an imaging framework that is able to accurately reconstruct multiple depths at individual pixels from single-photon observations. Our active imaging method models the single-photon detection statistics from multiple reflectors within a pixel, and it also exploits the fact that a multi-depth profile at each pixel can be expressed as a sparse signal. We interpret the multi-depth reconstruction problem as a sparse deconvolution problem using single-photon observations, create a convex problem through discretization and relaxation, and use a modified iterative shrinkage-thresholding algorithm to efficiently solve for the optimal multi-depth solution. We experimentally demonstrate that the proposed framework is able to accurately reconstruct the depth features of an object that is behind a partially-reflecting scatterer and 4 m away from the imager with root mean-square error of 11 cm, using only 19 signal photon detections per pixel in the presence of moderate background light. In terms of root mean-square error, this is a factor of 4.2 improvement over the conventional method of Gaussian-mixture fitting for multi-depth recovery.

Computational single-photon depth imaging without transverse regularization

“…This paper summarizes the imaging framework from [11,, [12,13] for pixelwise reconstruction of single depth and multiple depths per pixel using single-photon ToF data. In both settings, high photon efficiency is achieved using Poisson process photon detection modeling combined with sparsity of discrete-time flux vectors arising from longitudinal sparsity of reflectors.…”

“…In this paper, we present a pixelwise imaging framework from [11,, [12,13] for accurate depth-profile reconstruction using only a small number of photon detections in the presence of ambient background light. This framework achieves high photon efficiency using an accurate Poisson process model of photon detections and longitudinal sparsity constraints, based on discreteness of scene reflectors, but no transverse regularization.…”

“…Using simulations of single-photon LIDAR, we demonstrate that our proposed imaging framework outperforms the Gaussian-mixture fitting method, which is the conventional multidepth estimator assuming a large number of photon detections [17]. Experimental results are presented in [13]. Imaging setup with a raster-scanning pulsed source and a single-pixel single-photon detector for (top) single-reflector depth reconstruction and (bottom) multi-depth reconstruction (two-reflector case).…”

Restoration of multilayered single-photon 3D Lidar images

“…The resulting algorithm shows promising results, however, MCMC algorithms are known to be time-consuming which prevent their use in practical situations. Another algorithm has recently been proposed in [4] by considering a convex formulation coupled with an 1 sparsity promoting regularizer. This approach takes into account the Poisson statistics of the data and assumes the sparsity of the received photons.…”

“…Target reconstruction is obtained by minimizing a convex function composed of a data fidelity and regularization terms. The former is built based on the Poisson distribution of the observed photon counts and using a linear formulation similar to that proposed in [4]. Regarding the regularization terms, we first assume the presence of spatial correlation for each observed object, which is introduced using a convex total variation (TV) regularizer [5].…”