Optimized Structured Sparse Sensing Matrices for Compressive Sensing

TL;DR

This paper introduces a novel method for designing structured sparse sensing matrices that improve signal reconstruction in compressive sensing by minimizing mutual coherence and enhancing robustness.

Contribution

It proposes an optimization framework with an alternating minimization algorithm to design structured sparse sensing matrices with improved robustness and reconstruction performance.

Findings

Structured sensing matrices outperform random dense matrices in reconstruction accuracy.

The proposed method effectively minimizes mutual coherence and enhances robustness.

Numerical experiments demonstrate superior performance on synthetic and natural image data.

Abstract

We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix.