Compressed Sensing Based on Random Symmetric Bernoulli Matrix

TL;DR

This paper demonstrates that a partial random symmetric Bernoulli matrix, despite having dependent entries, can effectively serve as a measurement matrix in compressed sensing, offering a viable alternative to traditional independent-entry matrices.

Contribution

It introduces the use of a partial random symmetric Bernoulli matrix for compressed sensing, expanding the types of matrices that can be used successfully.

Findings

Successful recovery of signals using the proposed matrix

High probability of accurate signal reconstruction

Experimental validation of matrix effectiveness

Abstract

The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works focused on random matrices with entries drawn independently from certain probability distributions, in this paper we show that a partial random symmetric Bernoulli matrix whose entries are not independent, can be used to recover signal from observations successfully with high probability. The experimental results also show that the proposed matrix is a suitable measurement matrix.