Construction of compressive measurement matrix based on convolution of fractional chaos and cyclic matrix

A method is proposed to construct an improved measurement matrix—chaotic cyclic convolution measurement matrix (CCCMM). It is constructed by convoluting the fractional order Lorenz chaotic sequences and the cyclic matrix; since cyclic matrix is easy to implement on hardware, accurate reconstructed signal can be obtained by using fractional order chaos with pseudorandomness and convoluting them makes computing results smooth. Meanwhile, CCCMM is proved to have the high probability to satisfy the restricted isometry property. Then, the one-dimensional signals and two-dimensional images are simulated by the CCCMM and other methods, and the results show that the CCCMM is more superior in evaluating recovered signals with parameters and the visual effect of the restored images.