Design and Construction of High Performance Compressed Sensing Measurement Matrix

Design and Construction of High Performance Compressed Sensing Measurement Matrix

With the advancing application of compression theory in practical engineering problems, the hardware feasibility of the measurement matrix has gradually become an important factor in considering the comprehensive performance of the compressed sensing system. Although random matrix of independently identically distribution can be used as a universal CS measurement matrix due to its nearly incoherent nature with any signal, the hardware realization of the kind is hard to reach and tends to occupy large storage space. Thus, it is difficult to apply in resource-constrained scenarios. To solve this problem, an innovate Diagonal Toeplitz/Circulant structure block based sparse matrix is proposed in the paper. It then proves that the matrix satisfies the Restricted Isometry Property (RIP) conditions with a probability close to 1. The simulation experiments show that the measurement matric proposed in the paper can not only ensure the accurate reconstruction of sparse signals, but also greatly save the time required for measurement and reconstruction.