Thresholding Greedy Pursuit for Sparse Recovery Problems

TL;DR

This paper introduces Thresholding Greedy Pursuit (TGP), a thresholding-based algorithm for sparse recovery in noisy settings, which guarantees exact recovery without prior knowledge of sparsity or noise level as data dimension grows.

Contribution

The paper proposes TGP, a novel thresholding approach for sparse recovery that achieves exact recovery without needing sparsity or noise information.

Findings

TGP guarantees exact recovery with high probability in high dimensions.

Proper thresholding parameter choice is crucial for performance.

The method performs well even without prior sparsity or noise knowledge.

Abstract

We study here sparse recovery problems in the presence of additive noise. We analyze a thresholding version of the CoSaMP algorithm, named Thresholding Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding parameter, even without the knowledge of sparsity level of the signal and strength of the noise, can result in exact recovery with no false discoveries as the dimension of the data increases to infinity.