Statistical Mechanical Analysis of Compressed Sensing Utilizing Correlated Compression Matrix

TL;DR

This paper uses statistical mechanics to analyze how correlations in the compression matrix affect the reconstruction limits of compressed sensing, revealing that strong correlations slightly impair performance.

Contribution

It introduces a statistical mechanics framework to evaluate the impact of correlated compression matrices, specifically Kronecker-type, on compressed sensing reconstruction limits.

Findings

Strong one-dimensional correlations slightly degrade reconstruction performance

Correlated matrices modeled as Kronecker-type affect the reconstruction limit

Analysis provides insights into the design of compression matrices in compressed sensing

Abstract

We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix modeled as the Kronecker-type random matrix studied in research on multi-input multi-output wireless communication systems. We found that strong one-dimensional correlations between expansion bases of original information slightly degrade reconstruction performance.