Flexible construction of measurement matrices in compressed sensing based on extensions of incidence matrices of combinatorial designs

Abstract

In signal processing, compressed sensing (CS) can be used to acquire and reconstruct sparse signals. This paper presents a method of combining vertical expansions and horizontal expansions to construct measurement matrices. Firstly, we give a construction of (n,n,n−1,n−1,n−2)-BIBD based on finite set. It is important to estimate recovery performance of measurement matrices in terms of coherence, and it is found that the incidence matrix H of (n,n,n−1,n−1,n−2)-BIBD is not suitable as a measurement matrix in CS. We present an optimal method of combining vertical expansions and horizontal expansions for addressing this problem. These two extensions provide a new perspective for the construction of measurement matrices. Vertical expansions ensure that the matrix has low coherence. Horizontal expansions ensure that the matrix is more suitable as a measurement matrix in CS because of sizes and coherence. Finally, compared with several typical matrices, our matrices have better recovery performance under OMP and IST by the simulation experiments.