Blind Super-resolution via Projected Gradient Descent

TL;DR

This paper introduces a nonconvex method for blind super-resolution that leverages low rank matrix recovery of Hankel matrices, providing theoretical guarantees and demonstrating competitive performance through numerical experiments.

Contribution

It proposes a novel nonconvex approach for blind super-resolution based on low rank Hankel matrix recovery, with proven theoretical guarantees.

Findings

Method achieves accurate super-resolution results.

Theoretical guarantees comparable to convex methods.

Numerical experiments validate effectiveness.

Abstract

Blind super-resolution can be cast as low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient nonconvex method for this problem based on the low rank structure of the vectorized Hankel matrix associated with the target matrix. Theoretical guarantees have been established under the similar conditions as convex approaches. Numerical experiments are also conducted to demonstrate its performance.