Sensing Matrix Design via Capacity Maximization for Block Compressive Sensing Applications

TL;DR

This paper introduces a novel capacity maximization approach for designing sensing matrices that improve block-sparse signal reconstruction in compressive sensing applications, especially when randomization is limited.

Contribution

The paper proposes a new method for sensing matrix design based on capacity maximization, addressing practical constraints in measurement systems.

Findings

Enhanced reconstruction performance demonstrated in numerical examples.

Method significantly outperforms traditional random sensing matrices.

Applicable to electromagnetic imaging and similar CS applications.

Abstract

It is well established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as electromagnetic imaging, practical limitations on the measurement system prevent one from generating sensing matrices in this fashion. Although one can usually randomized the measurements to some degree, these sensing matrices do not achieve the same reconstruction performance as the truly randomized sensing matrices. In this paper, we present a novel method, based upon capacity maximization, for designing sensing matrices with enhanced block-sparse signal reconstruction capabilities. Through several numerical examples, we demonstrate how our method significantly enhances reconstruction performance.