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

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.