A new design criterion for optimal measurement matrix in compressed sensing systems

This paper deals with the optimal measurement matrix design problem for compressed sensing (CS) systems with a dictionary given. Such a problem is usually formulated as to minimize the distance between the Gram of the equivalent dictionary of the CS systems and a target Gram of nice properties. A new design criterion is proposed, which is defined in terms of three popularly used target Grams. An algorithm is derived to solve the corresponding design problem. Extensive experiments have been carried out and the simulation results have demonstrated the superiority of the new proposed method.