Forming images with focused, spatially resolved light is an area of rapid innovation due to the growing use of computational methods and the variety of meanings of ?image.? Aside from being photograph-like, an image acquired through optical means could show distances, thicknesses, chemical concentrations, molecular energy transfers and many other properties, depending on the methods of collection and analysis. In many settings, it is desirable to form images from very little detected light; collecting more light could take more energy, time, or space, or it could damage a biological or molecular sample under investigation. This project will develop new methods for computational image formation from very little detected light. The goals are both theoretical and practical: to understand the fundamental trade-offs between accuracy and amount of detected light, and to approach the best possible performance. The project has the potential to improve long-range remote sensing as well as various forms of microscopy.
The semiclassical model of light detection dictates that light field intensity translates to the rate of a Poisson process observed at a single-photon detector output. There are significant intellectual challenges in fully exploiting this prevailing model. While progress has been made in recent years to incorporate piecewise smoothness (e.g., wavelet-domain sparsity) and other structure that is commonly found in natural signals, this progress has largely relied on measurement likelihood functions being Gaussian. Signal processing methods designed for Poisson processes are uncommon, and most of them apply pointwise rather than to allow the inclusion of useful signal priors. Naive combinations of convex signal priors with Poisson likelihoods can lead to intractable nonconvex optimizations. This project will develop alternative approaches, especially toward real-time 3D acquisition.
