Noise Resilient Recovery Algorithm for Compressed Sensing

TL;DR

This paper introduces EMP, a noise-resilient greedy algorithm for compressed sensing that effectively recovers signals under high noise levels, even when sparsity is unknown or signals are compressible.

Contribution

The paper presents EMP, a novel entropy minimization based matching pursuit algorithm that improves noise robustness in compressed sensing recovery, especially under unknown sparsity conditions.

Findings

EMP outperforms traditional greedy algorithms in noisy environments.

The algorithm effectively recovers compressible signals with unknown sparsity.

Simulation results demonstrate enhanced noise rejection capabilities.

Abstract

In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or they estimate sparsity, for a known representation basis, from the number of measurements. These algorithms recover signals when noise level is significantly low. We propose Entropy minimization based Matching Pursuit (EMP) which has the capability to reject noise even when noise level is comparable to that of signal level. The proposed algorithm can cater to compressible signals and signals for which sparsity is not known in advance. Simulation study of the proposed scheme shows improved robustness to white Gaussian noise in comparison with the conventional greedy recovery algorithms.