Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields

Compressed Sensing (CS) is a new signal processing theory under the condition that the signal is sparse or compressible. One of the central problems in compressed sensing is the construction of sensing matrices. In this paper, we provide a new deterministic construction via vector spaces over finite fields, which is superior to Devore's construction using polynomials over finite fields under some conditions. Moreover, we use the algorithm to perform numerical simulation experiments on sensing matrices. Simulation results also demonstrate that signal recovery performance performs better using the constructed matrices as compared with several state-of-the-art sensing matrices, such as DeVore's matrix and random Gaussian matrix.