Approximate super-resolution of positive measures in all dimensions

Abstract

We study the problem of reconstructing a positive discrete measure on a compact set $K\subseteq {\mathbb{R}}^n$ from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.