A novel approach to sensing matrix optimization

This paper considers the problem of designing sensing matrix F for a compressive sensing (CS) system in which the dictionary ? is assumed to be given. A new measure is proposed for optimal sensing matrix design. 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. The optimal sensing matrix design problem is defined to identify those sensing matrices that minimize this measure and a closed-form solution is derived for solving such problem. 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.