A gradient-based algorithm for optimizing sensing matrix with normalization constraint

This paper deals with the problem of designing the sensing matrix Φ for a compressed sensing (CS) system, in which the dictionary Ψ is assumed to be given. The optimal sensing matrix design is formulated as to identify those Φ which minimize a proposed coherence-based measure with the constraint that the equivalent dictionary A = ΦΨ is normalized. Unlike the existing measures, the proposed measure is defined as the sum of lp-norm-based coherence factors. A gradient-based algorithm is derived for solving this problem. Experiments are carried out and simulations show that the sensing matrix obtained by the proposed algorithm significantly improves the signal recovery accuracy of the CS system and outperforms those by existing algorithms.