Sparse kronecker pascal measurement matrices for compressive imaging

Background: The construction of measurement matrix becomes a focus in compressed sensing (CS) theory. Although random matrices have been theoretically and practically shown to reconstruct signals, it is still necessary to study the more promising deterministic measurement matrix. Methods: In this paper, a new method to construct a simple and efficient deterministic measurement matrix, sparse kronecker pascal (SKP) measurement matrix, is proposed, which is based on the kronecker product and the pascal matrix. Results: Simulation results show that the reconstruction performance of the SKP measurement matrices is superior to that of the random Gaussian measurement matrices and random Bernoulli measurement matrices. Conclusions: The SKP measurement matrix can be applied to reconstruct high-dimensional signals such as natural images. And the reconstruction performance of the SKP measurement matrix with a proper pascal matrix outperforms the random measurement matrices.