Stable singularity detection from low-resolution data

The problem of computational super-resolution asks to recover “high-resolution features” of a signal from inaccurate and low-resolution data, using some kind of a-priori model as a regularization.  I will describe several situations for which sharp bounds for stable  reconstruction are known, depending on signal complexity, noise/uncertainty level, and available data bandwidth. I will also discuss optimal recovery algorithms, and some open questions.