Compressed Sensing Matrices: Binary vs. Ternary

TL;DR

This paper compares binary and ternary sensing matrices in compressed sensing, revealing that binary matrices generally outperform ternary ones when sharing the same sparsity and distribution of nonzero elements, based on RIP analysis and simulations.

Contribution

It provides the first comparative evaluation of binary versus ternary sensing matrices under identical sparsity and distribution conditions.

Findings

Binary matrices outperform ternary matrices in overall performance.

RIP analysis supports the superiority of binary matrices.

Numerical simulations confirm the analytical results.

Abstract

Binary matrix and ternary matrix are two types of popular sensing matrices in compressed sensing for their competitive performance and low computation. However, to the best of our knowledge, there seems no literature aiming at evaluating their performances if they hold the same sparisty, though it is of practical importance. Based on both RIP analysis and numerical simulations, this paper, for the first time, discloses that {0, 1} binary matrix holds better overall performance over {0, +1, -1} ternary matrix, if they share the same distribution on nonzero positions.