Construction of compressed sensing matrix based on complementary sequence

Abstract

We propose a new construction method for deterministic sensing matrix, using complementary sequence, which is called Compressed Sensing Matrix Based on Cyclic Complementary Sequence. Simulation results show that the reconstruction of this matrix better than sparse sensing matrices and Toeplitz matrices. Once the complementary sequences are given, each element in the matrix can be determined, and thus the uncertainty caused by using random matrices shall be avoided; moreover, the cyclic property of the matrix proposed makes it easier for hardware implementation and avoid the deficiency of taking up large storage space, which is universal for random matrices, and thus makes the matrix more practical.