A new method on deterministic construction of the measurement matrix in compressed sensing

TL;DR

This paper introduces a novel deterministic method for constructing measurement matrices in compressed sensing, addressing an open problem and demonstrating optimality based on mutual incoherence.

Contribution

It proposes a new deterministic construction technique for measurement matrices in compressed sensing, solving a longstanding open problem.

Findings

The new method is proven to be optimal in terms of mutual incoherence.

It provides a deterministic alternative to random matrix constructions.

The approach advances the theoretical foundation of measurement matrix design.

Abstract

Construction on the measurement matrix $A$ is a central problem in compressed sensing. Although using random matrices is proven optimal and successful in both theory and applications. A deterministic construction on the measurement matrix is still very important and interesting. In fact, it is still an open problem proposed by T. Tao. In this paper, we shall provide a new deterministic construction method and prove it is optimal with regard to the mutual incoherence.