Sensing matrix optimization for compressed sensing with consideration of sparse representation error and rank constraint

This paper deals with designing sensing matrix for a compressive sensing (CS) system with sparse representation error and rank constraint taken into account. Unlike the traditional design methods, the newly proposed measure takes the sparse representation error into account and hence is expected to lead to a more robust CS system. An alternative minimization based algorithm is derived for solving the optimal sensing matrix design without rank constraint. The rank constraint is then considered with a penalty term added in the proposed measure. A closed-form solution is derived for finding the optimal sensing matrix. Experiments are carried out and simulations show that the sensing matrix obtained by the proposed approach improves the signal recovery accuracy of the CS system greatly and outperforms those by existing algorithms when the sparse representation error is very high.