The ability of an active imaging system to accurately reconstruct scene properties in low light-level conditions has wide-ranging applications, spanning biological imaging of delicate samples to long-range remote sensing. Conventionally, even with time-resolved detectors that are sensitive to individual photons, obtaining accurate images requires hundreds of photon detections at each pixel to mitigate the shot noise inherent in photon-counting optical sensors.
In this thesis, we develop a computational imaging framework that allows accurate reconstruction of scene properties using small numbers of photons. This framework first probabilistically models the statistics of individual photon detections, which are observations of an inhomogeneous Poisson process, and expresses a priori scene constraints given a specific imaging problem. This yields an inverse problem that can be accurately solved using novel variations on sparse signal pursuit methods and regularized convex optimization techniques. We demonstrate our framework’s photon efficiency in six imaging scenarios that were previously well-studied in the classical regime with large numbers of photon detections: single-depth imaging, multi-depth imaging, array-based time-resolved imaging, super-resolution imaging, single-pixel imaging, and fluorescence imaging. Using simulations and experimental single-photon datasets, we show that our framework outperforms conventional imagers that use more naive observation models or scene models based on high light-level assumptions. For example, when imaging depth, reflectivity, or fluorescence, our implementation gives accurate reconstruction results even when the average number of signal photons at a pixel is less than 1, in the presence of extraneous background light.
Thesis supervisors: Prof. Jeffrey Shapiro and Prof. Vivek Goyal
Thesis committee members: Dr. Franco Wong and Prof. Bill Freeman