Structured Iterative Hard Thresholding with On- and Off-Grid Applications

TL;DR

This paper introduces a structured iterative hard thresholding algorithm for linear sparse recovery problems with known support structures, analyzing its convergence and applying it to inverse source problems including off-grid scenarios.

Contribution

It proposes a novel structured iterative hard thresholding method that incorporates support structure and analyzes its convergence and error bounds.

Findings

Algorithm effectively recovers structured sparse signals

Convergence depends on mutual coherence

Numerical simulations demonstrate off-grid recovery capabilities

Abstract

We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An algorithm based on iterative hard thresholding is proposed to solve this problem. The convergence and error of the method are analyzed with respect to mutual coherence. Numerical simulations are examined in the context of an inverse source problem, including modifications for off-grid recovery