Deterministic complex-valued measurement matrices based on Berlekamp-Justesen codes

Nowadays deterministic construction of measurement matrices is a hot topic in compressed sensing. In this paper, we propose two classes of deterministic complex-valued measurement matrices based on Berlekamp-Justesen codes. Row and column numbers of these matrices are tunable through row and column puncturing. Moreover, the proposed matrices are obtained from circular matrices, thus the storage costs of them are relatively low and both the sampling and recovery process can be simpler. Simulation results show that the proposed matrices perform better than Gaussian random matrices and some other deterministic measurement matrices under OMP recovery, especially for image reconstruction.