Deterministic construction of sparse binary and ternary matrices from existing binary sensing matrices

TL;DR

This paper presents a deterministic method for constructing sparse binary and ternary matrices from existing binary sensing matrices, enabling the creation of compressed sensing matrices with desirable properties for various row sizes.

Contribution

The authors introduce a novel deterministic construction technique for sparse matrices that supports flexible row sizes and improves computational efficiency in compressed sensing applications.

Findings

Constructed matrices have smaller density and support low-complexity algorithms.

Method allows for matrices with general row sizes beyond traditional prime power forms.

Demonstrated applicability to various compressed sensing scenarios.

Abstract

In the present work, we discuss a procedure for constructing sparse binary and ternary matrices from existing two binary sensing matrices. The matrices that we construct have several attractive properties such as smaller density, which supports algorithms with low computational complexity. As an application of our method, we show that a CS matrix of general row size different from $p, p^2, pq$ (for different primes $p,q$) can be constructed.