Deterministic Construction of Measurement Matrices Based on Bose Balanced Incomplete Block Designs

Compressed sensing is a novel information collection theory. Compared with the Nyquist sampling theorem, compressed sensing can obtain all the information of a signal with very few samples. The deterministic construction of the measurement matrix is an important research area in compressed sensing. Inspired by the observation that the parity-check matrix of low-density parity-check code can be used as a deterministic measurement matrix, in this paper, a special balanced incomplete block design proposed by Bose is exploited to construct the deterministic measurement matrix. The incidence matrix of the balanced incomplete block design proposed by Bose is used as the deterministic measurement matrix. The experimental results show that the proposed measurement matrix has lower mutual coherence than some widely used measurement matrices and shows better performance than the progressive edge-growth measurement matrix. Moreover, by using the embedding operation, the modified measurement matrix with a more flexible size and improved performance is constructed. In our simulation, the modified measurement matrix has lower mutual coherence and better performance than some widely used measurement matrices.