Support detection in super-resolution

TL;DR

This paper addresses the challenge of super-resolving point sources from noisy low-pass data, demonstrating that a convex optimization approach can accurately locate sources under certain separation and noise conditions.

Contribution

It introduces a convex program for support detection in super-resolution, providing theoretical guarantees for accurate source localization.

Findings

Supports accurate source localization when sources are separated by at least 2/f

High precision support detection is achievable with low noise levels

Convex optimization effectively solves the super-resolution support detection problem

Abstract

We study the problem of super-resolving a superposition of point sources from noisy low-pass data with a cut-off frequency f. Solving a tractable convex program is shown to locate the elements of the support with high precision as long as they are separated by 2/f and the noise level is small with respect to the amplitude of the signal.