Speaker: Weilin Li from CUNY

Title. Super-resolution: theory and algorithms.

Abstract. The Rayleigh length in optics refers to the minimum distance between two particles that can be resolved by an imaging system. Although this is a widely used principle, there is experiment evidence that in certain situations, there are no fundamental resolution limits. Motivated by such discoveries, we examine this phenomenon from a mathematical viewpoint. Super-resolution asks whether it is possible to stably recover point sources, possibly closer than the Rayleigh length, from noisy Fourier measurements. We study the fundamental limits of super-resolution from an information theoretic viewpoint and the stability of subspace methods such as ESPRIT. We derive novel multiscale lower bounds for the minimum singular value of Fourier/Vandermonde matrices and a perturbation bound for subspace algorithms that depends on the local geometry of the point sources. These results indicate that it is possible to bypass the resolution limit in an almost optimal way.