Incoherent Projection Matrix Design for Compressed Sensing Using Alternating Optimization

In this paper we address the design of projection matrix for compressed sensing. In most compressed sensing applications, random projection matrices have been used but it has been shown that optimizing these projections can greatly improve the sparse signal reconstruction performance. An incoherent projection matrix can greatly reduce the recovery error for sparse signal reconstruction. With this motivation, we propose an algorithm for the construction of an incoherent projection matrix with respect to the designed equiangular tight frame (ETF) for reducing pairwise mutual coherence. The designed frame consists of a set of column vectors in a finite dimensional Hilbert space with the desired norm and reduced pairwise mutual coherence. The proposed method is based on updating ETF with inertial force and constructing incoherent frame and projection matrix using alternating minimization. We compare the performance of the proposed algorithm with state-of-the-art projection matrix design algorithms via numerical experiments and the results show that the proposed algorithm outperforms the other algorithms.