An Alternative Thresholding Rule for Compressed Sensing

TL;DR

This paper introduces Look Ahead Thresholding, a new rule for compressed sensing that incorporates problem-specific information, improving the traditional hard thresholding approach through theoretical and experimental validation.

Contribution

The paper proposes Look Ahead Thresholding, an innovative thresholding method that adapts to specific problem instances, enhancing compressed sensing performance.

Findings

Theoretical analysis supports the effectiveness of Look Ahead Thresholding.

Experimental results demonstrate improved sparse recovery accuracy.

The new rule outperforms traditional hard thresholding in various scenarios.

Abstract

Compressed Sensing algorithms often make use of the hard thresholding operator to pass from dense vectors to their best s-sparse approximations. However, the output of the hard thresholding operator does not depend on any information from a particular problem instance. We propose an alternative thresholding rule, Look Ahead Thresholding, that does. In this paper we offer both theoretical and experimental justification for the use of this new thresholding rule throughout compressed sensing.