Photon-Efficient Computational 3-D and Reflectivity Imaging With Single-Photon Detectors

Abstract

Capturing depth and reflectivity images at low light levels from active illumination of a scene has wide-ranging applications. Conventionally, even with detectors sensitive to individual photons, hundreds of photon detections are needed at each pixel to mitigate Poisson noise. We develop a robust method for estimating depth and reflectivity using fixed dwell time per pixel and on the order of one detected photon per pixel averaged over the scene. Our computational image formation method combines physically accurate single-photon counting statistics with exploitation of the spatial correlations present in real-world reflectivity and 3-D structure. Experiments conducted in the presence of strong background light demonstrate that our method is able to accurately recover scene depth and reflectivity, while traditional imaging methods based on maximum likelihood (ML) estimation or approximations thereof lead to noisier images. For depth, performance compares favorably to signal-independent noise removal algorithms such as median filtering or block-matching and 3-D filtering (BM3D) applied to the pixelwise ML estimate; for reflectivity, performance is similar to signal-dependent noise removal algorithms such as Poisson nonlocal sparse PCA and BM3D with variance-stabilizing transformation. Our framework increases photon efficiency 100-fold over traditional processing and also improves, somewhat, upon first-photon imaging under a total acquisition time constraint in raster-scanned operation. Thus, our new imager will be useful for rapid, low-power, and noise-tolerant active optical imaging, and its fixed dwell time will facilitate parallelization through use of a detector array.Index Terms-3-D imaging, computational imaging, convex optimization, first-photon imaging, LIDAR, low-light imaging, Poisson noise, single-photon detection, time-of-flight imaging.

Photon-efficient super-resolution laser radar

“…This is not a low number of photons per pixel comparable to recent works in which deconvolution is not needed, [14][15][16][17] but the results suggest that it is low enough that our explicit Poissonian modeling of observed photon counts improves performance. The flattened photon data cube f (Y) ∈ N nxny×nt is illustrated in image form in Fig.…”

“…[15][16][17] One core assumption behind these existing lowlight depth imaging frameworks is that the spatial spot size of the illumination is small enough that we can assume that each pixel measurement has addressed a different scene patch. However, in practice, this independent-pixel assumption can break down due to non-idealities in the illumination source and imaging conditions.…”

Bayesian restoration of reflectivity and range profiles from subsampled single-photon multispectral Lidar data

“…In a similar fashion to [5], [10], [17], we simplify the problem by estimating sequentially Λ and T, using weak assumptions which can often be satisfied in practice. The two estimation steps are detailed in what follows.…”

Computational single-photon depth imaging without transverse regularization

“…Very recently, computational imaging frameworks have been introduced to process photon detection data without treating a detection-time histogram as approximating a flux waveform, and using regularization predicated on piecewise smoothness in the transverse dimensions [6][7][8][9][10]. For natural scenes, accurate results have been demonstrated from as little as 1 detected photon per pixel, even in the presence of significant ambient light.…”