Robust projection matrix optimization from the MSE view for compressive sensing systems

It's well known that sparse signals can be sensed with a reduced number of projections and then reconstructed if compressive sensing (CS) is employed. We consider the problem of designing the projection matrix Φ for a compressive sensing system in which the dictionary Ψ is assumed to be given. Moreover, we consider the more general case in which the measurements are contaminated by white Gaussian noise. A novel robust algorithm based on regular minimization from the Mean Square Error(MSE) view for optimal projection matrix searching is proposed to solve the corresponding minimization problem. Simulation results reveal that the signal recovery performance of sensing matrix obtained by the proposed algorithm surpasses that achieved by other existing sensing matrix design methods.