Projection matrix design using prior information in compressive sensing

This paper proposes a projection matrix design algorithm using prior information on sparse signal to reduce local cumulative coherence, since small local coherence can improve the sparse signal recovery rate. Local cumulative coherence describes the coherence between the atoms indexed by the support of the sparse signal and other atoms. Using prior information on the sparse signal, projection matrix design is formulated as an optimization problem that minimizes the weighted Frobenius distance between the Gram matrix and the identity matrix. This optimization problem is solved by majorization–minimization method, which iteratively minimizes the surrogate function. If the prior information is accurate, the designed projection matrix can make the local cumulative coherence small. Numerical experiments on both synthesized signals and real image sequences demonstrate the effectiveness of the proposed algorithm in improving the performance of sparse signal recovery algorithms such as greedy algorithms and basis pursuit algorithm.