On the Modulus of Continuity for Noisy Positive Super-Resolution

Abstract

This paper considers the problem of super-resolution with positive constraints. By utilizing the concept of Modulus of Continuity (MC), we propose a unified framework for analyzing the robustness of super-resolution reconstruction in presence of noise, which is algorithm-independent and emphasizes the role of signal structures. In contrast to earlier works, we show that incorporation of positive constraints improves the scaling factor of MC and provides tighter upper bound on the estimation error of any algorithm that exploits such structure. The unified framework is further applied to analyze convex algorithms for positive super-resolution, and the theoretical results are validated by numerical experiments.