Compressed synthetic aperture radar with structurally sparse random matrices

Abstract

A revolutionary signal sampling framework called compressed sensing (CS) has been proposed to solve the problem of high storage and transmission burden in synthetic aperture radar (SAR) imaging system. An undetermined measurement matrix can capture sparse signals losslessly if the matrix satisfies the restricted isometry property (RIP) in CS. However, existing measurement matrices suffer from high computational burden because of their completely unstructured nature. In this study, the authors propose to construct a novel measurement matrix with a specific structure, called structurally sparse random matrix (SSRM), to reduce the computational burden. The RIP of the proposed SSRM is also guaranteed with overwhelming probability. The simulation results validate that SSRM reduces the computational burden significantly whereas keeps similar signal recovery accuracy as Gaussian random matrices.