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.This material is based upon work supported in part by a Samsung Scholarship, the US National Science Foundation under Grant No. 1422034, and the MIT Lincoln Laboratory Advanced Concepts Committee. We thank Dheera Venkatraman for his assistance with the experiments. (Samsung Scholarship; 1422034 - US National Science Foundation; MIT Lincoln Laboratory Advanced Concepts Committee)Accepted manuscrip