Mixed Compressed Sensing Based on Random Graphs

TL;DR

This paper introduces a novel class of structured measurement matrices for compressed sensing based on mixed symmetric random graphs, demonstrating their effectiveness in signal recovery.

Contribution

It proposes a new type of measurement matrix derived from random graph models with mixed distributions, expanding the options for structured compressed sensing matrices.

Findings

Mixed symmetric random matrices enable successful signal recovery.

High probability of recovery with the proposed matrices.

Structured matrices derived from random graphs are effective in compressed sensing.

Abstract

Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and recover signal well, in most cases, we hope the measurement matrix imposed with some special structure. In this paper, based on random graph models, we show that the mixed symmetric random matrices, whose diagonal entries obey a distribution and non-diagonal entries obey another distribution, can be used to recover signal successfully with high probability.