Low coherence deterministic matrices construction using Hash functions

Deterministic measurement matrices have a crucial character in compressive sensing (CS) applications. These matrices can be generated randomly and deterministically. Due to less memory needed for storage, deterministic matrices have been taken into consideration vastly rather than random ones. In this paper, by use of Hash functions (HF), a group of new measurement matrices has been presented. For this purpose, first, a primary matrix of code is generated then by use of Hash matrices a new matrix is produced. Finally by normalizing the new matrix elements, measurement matrix will be generated. Through this construction, a group of measurement matrices with size of 2 3 p p  and coherence coefficient equal to1 p , where p is a prime integer, will be obtained. Simulation results illustrate that for low values of p , proposed matrices slightly outweigh BCH sampling matrices.