Dongeek Shin

First-Photon Imaging

Computing an Image Firing off a burst of laser pulses and detecting the back-reflected photons is a widely used method for constructing three-dimensional (3D) images of a scene. Kirmani et al. (p. 58, published online 29 November) describe an active imaging method in which pulsed laser light raster scans a scene and a single-photon detector is used to detect the first photon of the back-reflected laser light. Exploiting spatial correlations of photons scattered from different parts of the scene allows computation of a 3D image. Importantly, for biological applications, the technique allows the laser power to be reduced without sacrificing image quality. A computational imaging method based on photon timing enables three-dimensional imaging under low light flux conditions. Imagers that use their own illumination can capture three-dimensional (3D) structure and reflectivity information. With photon-counting detectors, images can be acquired at extremely low photon fluxes. To suppress the Poisson noise inherent in low-flux operation, such imagers typically require hundreds of detected photons per pixel for accurate range and reflectivity determination. We introduce a low-flux imaging technique, called first-photon imaging, which is a computational imager that exploits spatial correlations found in real-world scenes and the physics of low-flux measurements. Our technique recovers 3D structure and reflectivity from the first detected photon at each pixel. We demonstrate simultaneous acquisition of sub–pulse duration range and 4-bit reflectivity information in the presence of high background noise. First-photon imaging may be of considerable value to both microscopy and remote sensing.

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

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.

Computational multi-depth single-photon imaging

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.

Computational 3D and reflectivity imaging with high photon efficiency

Capturing depth and reflectivity images at low light levels from active illumination of a scene has wide-ranging applications. Conventionally, even with single-photon detectors, hundreds of photon detections are needed at each pixel to mitigate Poisson noise. We introduce a robust method for estimating depth and reflectivity using on the order of 1 detected photon per pixel averaged over the scene. Our computational imager combines physically accurate single-photon counting statistics with exploitation of the spatial correlations present in real-world reflectivity and 3D structure. Experiments conducted in the presence of strong background light demonstrate that our computational imager is able to accurately recover scene depth and reflectivity, while traditional maximum likelihood-based imaging methods lead to estimates that are highly noisy. Our framework increases photon efficiency 100-fold over traditional processing and thus will be useful for rapid, low-power, and noise-tolerant active optical imaging.

Parametric Poisson process imaging

In conventional 3D imaging, a large number of detected photons is required at each pixel to mitigate the effect of signal-dependent Poisson or shot noise. Parametric Poisson process imaging (PPPI) is a new framework that enables scene depth acquisition with very few detected photons despite significant contribution from background light. Our proposed computational imager is based on accurate physical modeling of the photon detection process using time-inhomogeneous Poisson processes combined with regularization that promotes piecewise smoothness. Simulations demonstrate accurate imaging with only 1 detected photon per pixel.

Spatio-temporal regularization for range imaging with high photon efficiency

Conventional depth imagers using time-of-flight methods collect hundreds to thousands of detected photons per pixel to form high-quality depth images of a scene. Through spatio-temporal regularization achieved with maximum a posteriori probability estimation under a scene prior and an inhomogeneous Poisson process likelihood function, we form depth images with dramatically higher photon efficiency even as low as one detected photon per pixel. Simulations demonstrate the combination of high accuracy and high photon efficiency of our method, compared to the traditional maximum likelihood estimate of the depth image and other popular denoising algorithms.

Photon-efficient computational imaging with a single-photon camera

Using a photon-efficient reconstruction algorithm and a single-photon camera prototype, we demonstrate accurate depth and reflectivity imaging of natural scenes from an average of ~1 detected signal photon per pixel.

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

Light detection and ranging systems reconstruct scene depth from time-of-flight measurements. For low light-level 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 union-of-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 computationally-efficient approximation to the maximum-likelihood solution, by a factor of 6.1 in absolute depth error.

Low-rate Poisson intensity estimation using multiplexed imaging

Multiplexed imaging is a powerful mechanism for achieving high signal-to-noise ratio (SNR) in the presence of signal-independent additive noise. However, for imaging in presence of only signal-dependent shot noise, multiplexing has been shown to significantly degrade SNR. Hence, multiplexing to increase SNR in presence of Poisson noise is normally thought to be infeasible. In this paper, we present an exception to this view by demonstrating multiplexing advantage when the scene parameters are non-negative valued and are observed through a low-rate Poisson channel.

Performance Analysis of Low-Flux Least-Squares Single-Pixel Imaging

A single-pixel camera is able to computationally form spatially resolved images using one photodetector and a spatial light modulator. The images it produces in low-light-level operation are imperfect, even when the number of measurements exceeds the number of pixels, because its photodetection measurements are corrupted by Poisson noise. Conventional performance analysis for single-pixel imaging generates estimates of mean-square error (MSE) from Monte Carlo simulations, which require long computational times. In this letter, we use random matrix theory to develop a closed-form approximation to the MSE of the widely used least-squares inversion method for Poisson noise-limited single-pixel imaging. We present numerical experiments that validate our approximation and a motivating example showing how our framework can be used to answer practical optical design questions for a single-pixel camera.