Optimizing projection matrix for compressed sensing systems

In this paper, a new method is proposed to optimize the projection matrix, which, unlike the existing approaches, attempts to choose the projection matrix such that the sensing matrix is as close to a tight frame/equiangular tight frame as possible. In the proposed method, there are two important procedures that are used to adjust the Gram matrix of the sensing matrix. The simulation results are presented to verify the validity of proposed approach with the basic pursuit (BP) and orthogonal match pursuit (OMP) algorithms used in signal reconstruction as well as to illustrate the promising potential of the proposed method.