Compressed sensing with combinatorial designs: theory and simulations

TL;DR

This paper analyzes a new combinatorial design-based construction for compressed sensing matrices, providing theoretical insights, simulation results, and a specialized recovery algorithm, demonstrating competitiveness with Gaussian matrices and noise tolerance.

Contribution

It offers a novel deterministic construction for compressed sensing matrices using combinatorial design theory, along with theoretical analysis and a tailored recovery algorithm.

Findings

Construction is competitive with Gaussian random matrices

Recovery is tolerant to noise

New tailored recovery algorithm improves performance

Abstract

In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the performance of matrices obtained from this construction. We provide new theoretical results and detailed simulations. These simulations indicate that the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. A new recovery algorithm tailored to the construction is also given.