Structural Scrambling of Circulant Matrices for Cost-effective Compressive Sensing

Compressed sensing (CS) is a promising theory that is able to measure signal below the Nyquist rate through measurement matrices. Random matrices are regarded as optimal measurement matrices to spread out signals to a small number of measurements. However, the random matrices cost too much memory space for implementation. The structured matrices are then proposed to reduce such enormous memory cost. Nevertheless, the recovery performance of the structured matrices suffers from severe degradation. In this paper, we propose sign-flipped scrambling method and extended-select scrambling method for circulant matrices to compensate the performance loss. The sign-flipped scrambling for circulant matrices is able to approach recovery performance of random matrices within defined guarantee region. On the other hand, the extended-select scrambling together with sign-flipped scrambling for circulant matrices is able to approximate the overall recovery performance of the random matrices. In addition, architectures are designed to realize the proposed scrambling methods. Compared with random matrices, proposed scrambling matrices are more cost-effective for implementation.