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.
Highlights
The ability to acquire 3D structure of a scene is important in many applications, such as biometrics [1], terrestrial mapping [2], and gaming [3]
We show that the multi-depth estimation problem from single-photon observations can be reformulated as a convex optimization problem by combining the statistics of photon detection data with sparsity of multi-depth profiles
We focus on comparing two algorithms: the mixture of Gaussians (MoG)-based estimator using a greedy histogram-data-fitting strategy and our proposed imager using convex optimization
Summary
The ability to acquire 3D structure of a scene is important in many applications, such as biometrics [1], terrestrial mapping [2], and gaming [3]. Given a pulsed illumination source, time histogramming methods of the photon detections from the backreflected pulse waveform have been used for pixelwise reconstruction of scene depths using single-photon imagers [16, 17]. For low-flux multi-depth imaging of scene reflectors in particular, one may choose to identify the peaks in the photon histogram by brute-force search over time bins Since this leads to a large processing time (polynomial in the number of time bins, with degree equal to the number of depths), fast algorithms using parametric deconvolution or finite-rate-of-innovation methods have been developed [19, 20]. The previously described multi-depth imaging methods using single-photon detectors only give accurate results when the image acquisition time is long enough that the number of photon detections is sufficiently high to form an accurate histogram. By adapting the iterative shrinkage-thresholding algorithm (ISTA) [25, 26] used for robust sparse signal pursuit to our single-photon imaging setup, we accurately solve for the global optimum of the convex optimization problem to obtain a multi-depth solution from a small number of photon detections
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
