Computational imaging with small numbers of photons

Abstract

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 timeresolved 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 computational imaging frameworks that allow accurate reconstruction of scene properties using small numbers of photons. These frameworks first model the statistics of individual photon detections, which are observations of an inhomogeneous Poisson process, and express a priori scene constraints for the specific imaging problem. Each 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 frameworks' photon efficiencies in six imaging scenarios that have been well-studied in the classical settings with large numbers of photon detections: single-depth imaging, multi-depth imaging, array-based timeresolved imaging, super-resolution imaging, single-pixel imaging, and fluorescence imaging. Using simulations and experimental datasets, we show that our frameworks outperform conventional imagers that use more naive observation models based on high light-level assumptions. For example, when imaging depth, reflectivity, or fluorescence lifetime, our implementation gives accurate reconstruction results even when the average number of detected signal photons at a pixel is less than 1, in the presence of extraneous background light.