Local recovery bounds for prior support constrained Compressed Sensing

TL;DR

This paper introduces local recovery bounds in prior support constrained compressed sensing, focusing on guarantees within the known support rather than full support, and analyzes conditions for small recovery error.

Contribution

It provides the first analysis of local recovery guarantees in prior support constrained compressed sensing, highlighting conditions for effective support-limited recovery.

Findings

Established local recovery bounds for prior support constrained compressed sensing

Identified parameter conditions ensuring small recovery errors

Differentiated local bounds from traditional global recovery guarantees

Abstract

Prior support constrained compressed sensing has of late become popular due to its potential for applications. The existing results on recovery guarantees provide global recovery bounds in the sense that they deal with full support. However, in some applications, one might be interested in the recovery guarantees limited to the given prior support, such bounds may be termed as local recovery bounds. The present work proposes the local recovery guarantees and analyzes the conditions on associated parameters that make recovery error small.