Blocked Polynomial Deterministic Matrix for Compressed Sensing

Abstract-Compressed Sensing (CS), a new area of signal processing, seeks to reconstruct sparse or compressible signal from a small number of measurements. Mostly, random matrix is used as measurement matrix, such as Gaussian, Bernoulli and Fourier matrices. However, those matrices are difficult to implement in hardware, so deterministic matrices are proposed, such as polynomial deterministic matrix. In this paper, we proposed blocked polynomial deterministic matrix, and proved that it satisfied the Restricted Isometry Property (RIP). Also, the proposed matrix has several advantages in CS applications: (i) The time of constructing matrix is shorter and the space to store the matrix is smaller compared with polynomial deterministic matrix; (ii) It can broaden the range of measurement number. Experimental results demonstrate that the proposed matrix is useful in CS applications.