A New Approach to Design Sensing Matrix Based on the Sparsity Constant With Applications to Computed Tomography

Abstract

Using random sensing matrices imposes some constraints on applying compressed sensing in practical applications such as computed tomography, high resolution radars, synthetic aperture radars and other imaging systems. On the other hand, the lack of certain criteria to measure the suitability of a sensing matrix in compressed sensing, makes designing of the relevant sampling system difficult; so, researchers have turned largely toward trial and error methods for designing such sensing matrices. In this paper, we propose a constructive approach to design measurement matrices which largely overcomes the aforementioned drawbacks and presents some simple and calculable measures for sensing matrices. The presented algorithm outperforms various random and deterministic approaches in designing compressed sensing matrices due to its recoverability performance and generality, at the same time, our scheme benefits from the fact that the sensing matrix performance is easily determined. Based on the proposed method and despite all constrains that exist in measurement matrices in different problems, we can design sensing matrices in a unified manner with even better performance than that of random scenarios. In addition, we apply the proposed algorithm in computed tomography where the measurement matrix is a structured matrix and our method can gain much improvement in the recoverability performance. Furthermore, this article provides parameters that affect the performance of a sensing matrix, which theoretically clarifies the causes of the good recoverability performance of Gaussian matrices and the poor recoverability performance of periodic matrices.