Photon-Efficient Full-Waveform Laser Radar Using a Single-Photon Detector

Full-waveform laser radar is an active 3D imaging framework that can be used to recover the complete depth profile of a complex scene (e.g., a natural forest) by analyzing multiple returns at every image pixel [1]. To mitigate the effect of shot noise in a photon-counting laser radar, conventional full-waveform imaging methods require histograms constructed from a large number of photon detections so that the depths of multiple reflectors can be accurately identified without undue computational burden [2]. We present a full-waveform imaging framework that allows fast and robust recovery of depth profiles using only a few photon detections at each image pixel. Our framework succeeds because it uses a physically-correct model for the pixelwise photon-detection statistics from multiple reflectors in the scene, and it exploits the fact that depth profiles of natural scenes can be expressed as sparse signals. We thus interpret the pixelwise fullwaveform imaging problem as one of sparse spike-signal estimation from single-photon observations. We prove that this sparse spike-signal estimation problem is a convex optimization; hence it can be solved efficiently using simple gradient-descent procedures [3]. After recovering the spike signal by solving the optimization problem, we apply thresholding on the amplitude of each spike to filter out residual spikes that are presumed to be extraneous. The final remaining spikes are our estimates of reflector depths at an image pixel. To benchmark our proposed 3D imaging framework against existing methods, we used the single-photon observation data that was collected by Dheera Venkatraman for the First-Photon Imaging project [4]. Those measurements used a 640 nm, 0.6 mW laser to repeatedly illuminate a laboratory scene with 200 ps duration pulses at a 100 ns repetition period. Photon-counting records, time stamped in 8 ps bins, were collected with a single-photon avalanche diode as the tightly-focused laser beam was scanned across the field of regard by a twoaxis scanning galvanometer. Light from an incandescent lamp generated unwanted background counts whose presence can lead to anomalous depth estimates. For benchmarking, we reconstructed the spatially-resolved depth profile by pixelwise use of our spike-signal-estimation framework, and compared its performance with that of conventional pixelwise maximum-likelihood (ML) processing. Figure 1 compares the reconstructions we obtained from imaging a sunflower object. In this experiment, the average photon count per pixel was approximately 10, with the average background-light count rate being approximately equal to the average laser-return count rate. We see that the conventional ML 3D estimate is corrupted by: (1) mixed-pixel artifacts that exist at depth boundaries between the flower and the wall behind it; and (2) extraneous counts from background light. Our imaging framework, however, successfully rejects both mixed-pixel artifacts and background counts. Moreover, the average per-pixel computational time of our pixelwise full-waveform estimator was less than 1 ms running in MATLAB on a standard laptop, making our framework applicable for practical real-time, low-light level 3D imaging scenarios. Increased reconstruction accuracy might be obtained by combining our framework with state-of-the-art 3D denoising techniques.