Improved Measurement Matrix and Reconstruction Algorithm for Compressed Sensing

In this paper, a new class of measurement matrices based on the complementary sequences is proposed for compressed sensing (CS). In contrast to the Hadamard matrix and Gaussian random measurement matrix, the advantages of the new scheme are the improvement of performance and the reduction of complexity. As a well-known recovery algorithm in CS, Orthogonal Matching Pursuit (OMP) is constrained by high computational cost, thus on the basis of this algorithm we extend the idea of Householder transformation to illustrate another recovery algorithm called HOMP. It is shown that HOMP can effectively reduce the reconstruction time with almost the same results as those by using the original method.