Multi-Sparse Signal Recovery for Compressive Sensing

TL;DR

This paper introduces a novel convex programming model that leverages multi-domain sparsity to enhance signal recovery in compressive sensing, demonstrating improved performance especially for signals sparse in multiple domains.

Contribution

It proposes a new convex optimization approach utilizing multi-sparsity constraints, advancing beyond traditional single-domain sparsity methods.

Findings

The method outperforms classical approaches in reconstructing multi-sparse signals.

Numerical experiments with EMG signals show improved recovery accuracy.

The approach effectively exploits sparsity in multiple domains for better results.

Abstract

Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains. To further improve the signal reconstruction performance, we can exploit this multi-sparsity to generate a new convex programming model. The latter is formulated with multiple sparsity constraints in multiple domains and the linear measurement fitting constraint. It improves signal recovery performance by additional a priori information. Since some EMG signals exhibit sparsity both in time and frequency domains, we take them as example in numerical experiments. Results show that the newly proposed method achieves better performance for multi-sparse signals.