Joint rank and positive semidefinite constrained optimization for projection matrix

Sparse signals can be sensed with a reduced number of projections and then reconstructed if compressive sensing is employed. Traditionally, the projection matrix is chosen as a random matrix, but a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy. This paper considers the problem of designing the projection matrix Φ for a compressive sensing system in which the dictionary Ψ is assumed to be given. A novel algorithm based on joint rank and positive semidefinite constrained optimization for optimal projection matrix searching is proposed. Simulation results reveal that the signal recovery performance of sensing matrix obtained by proposed algorithm surpasses that of other standard sensing matrix designs.