Single-Photon Depth Imaging Using a Union-of-Subspaces Model

Abstract

Abstract-Light detection and ranging systems reconstruct scene depth from time-of-flight measurements. For low lightlevel depth imaging applications, such as remote sensing and robot vision, these systems use single-photon detectors that resolve individual photon arrivals. Even so, they must detect a large number of photons to mitigate Poisson shot noise and reject anomalous photon detections from background light. We introduce a novel framework for accurate depth imaging using a small number of detected photons in the presence of an unknown amount of background light that may vary spatially. It employs a Poisson observation model for the photon detections plus a unionof-subspaces constraint on the discrete-time flux from the scene at any single pixel. Together, they enable a greedy signal-pursuit algorithm to rapidly and simultaneously converge on accurate estimates of scene depth and background flux, without any assumptions on spatial correlations of the depth or background flux. Using experimental single-photon data, we demonstrate that our proposed framework recovers depth features with 1.7 cm absolute error, using 15 photons per image pixel and an illumination pulse with 6.7-cm scaled root-mean-square length. We also show that our framework outperforms the conventional pixelwise log-matched filtering, which is a computationallyefficient approximation to the maximum-likelihood solution, by a factor of 6.1 in absolute depth error.

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 log-matched filtering, which is the conventional maximum-likelihood (ML) depth estimator in the absence of background flux [15]. Experimental results are presented in [12].…”

Optimal Stopping Times for Estimating Bernoulli Parameters with Applications to Active Imaging

“…Spatial correlations are used to regularize the estimation of the full scene reflectivity image, resulting in good performance from only 1 detected photon per pixel, even when half of the detected photons are attributable to uninformative ambient light. Comparing first-photon imaging to photon-efficient methods with deterministic dwell time [2,[13][14][15][16][17][18][19][20][21] was an initial inspiration for this work. To the best of our knowledge, no previous paper has explained an advantage or disadvantage from variable dwell time.…”

Photon-efficient imaging with a single-photon camera

“…Unlike prior work, our framework achieves high photon efficiency by exploiting the scene's structural information in both the transverse and the longitudinal domains to censor extraneous (background light and dark count) detections from the SPAD array. Earlier works that exploit longitudinal sparsity only in a pixel-by-pixel manner require more detected signal photons to produce accurate estimates 26 27 . Because our new imager achieves highly photon-efficient imaging in a short data-acquisition time, it paves the way for dynamic and noise-tolerant active optical imaging applications in science and technology.…”