Blind super-resolution of point sources via fast iterative hard thresholding

TL;DR

This paper introduces a fast, provable algorithm for blind super-resolution that leverages low rank Hankel matrix structures, demonstrating linear convergence and effectiveness through theoretical analysis and numerical experiments.

Contribution

The paper presents a novel fast iterative hard thresholding algorithm for blind super-resolution with proven linear convergence based on low rank Hankel matrix structures.

Findings

Algorithm converges linearly to the ground truth.

Numerical experiments confirm effectiveness and convergence.

Method outperforms existing approaches in speed and accuracy.

Abstract

In this work, we develop a provable fast algorithm for blind super-resolution based on the low rank structure of vectorized Hankel matrix associated with the target matrix. Theoretical results show that the proposed method converges to the ground truth with linear convergence rate. Numerical experiments are also conducted to illustrate the linear convergence and effectiveness of the proposed approach.