The Dark Side of Image Reconstruction: Emerging Methods in Photon-Limited Imaging

Many scientific and engineering applications rely upon the accurate reconstruction of spatially, spectrally, and temporally distributed phenomena from photon-limited data. When the number of observed events is very small, accurately extracting knowledge from this data requires the development of both new computational methods and novel theoretical analysis frameworks. This task is particularly challenging since sensing is often indirect in nature, such as in compressed sensing or with tomographic pro jections in medical imaging, resulting in complicated inverse problems. Furthermore, limited system resources, such as data acquisition time and sensor array size, lead to complex tradeoffs between sensing and processing. All of these issues combine to make accurate image reconstruction a complicated task, involving a myriad of system-level and algorithmic tradeoffs.

In this talk, I will describe novel algorithms and performance tradeoffs between
the underlying intensity exhibits some low-dimensional structure. The theory supporting these methods facilitates characterization of fundamental performance limits. Examples include lower bounds on the best achievable error performance in photon-limited image reconstruction and upper bounds on the data acquisition time required to achieve a target reconstruction accuracy. The effectiveness of the theory and methods will be demonstrated for several important applications, including astronomy, night vision, and biological imaging.