Design of an ordered Gaussian circular measurement matrix and analysis of its property

For one-dimensional signal, by combining the characteristics of its coefficients distribution in sparse domain, an ordered Gaussian circular measurement matrix was proposed and proved that it would satisfy the restricted isometry property in certain probability. The measurement matrix was formed by the extension and circulation of an ordered Gaussian sequence, the sampling of significant coefficients of signals were strengthened by the uneven distribution of measurement coefficients. The simulation results show that, compared with the random Gaussian measurement matrix and Toeplitz measurement matrix, the ordered Gaussian circular measurement matrix reduces the number of random elements effectively, which covercomes the difficulty of hardware implementation. Meanwhile, it improves the matching degree of the one-dimensional signal reconstruction from its projection, and maintains the properties of the two-dimensional image signal reconstruction at a comparable level.