Robust Projection Matrix Design and Its Application in Compression

The aim of this brief is to design a robust projection matrix for the Compressive Sensing (CS) system when the signal is not exactly sparse. The optimal projection matrix design is obtained by minimizing the Frobenius norm of the difference between the identity matrix and the Gram matrix of the equivalent dictionary $\Phi\Psi$. A novel penalty $\|\Phi\|_F$ is added to make the projection matrix robust when the sparse representation error (SRE) exists. Additionally, designing the projection matrix with a high dimensional dictionary improves the signal reconstruct accuracy when the compression rate is the same as in a low dimensional dictionary scenario. Simulation results demonstrate the effectiveness of the proposed approach comparing with the state-of-the-art methods.