Measurement-Driven Framework with Simultaneous Sensing Matrix and Dictionary Optimization for Compressed Sensing

Abstract

This paper presents a measurement-driven framework to deal with the compressed sensing (CS) system design problem. Under this novel framework, the sparse coefficient matrix is calculated according to the low-dimension measurements, rather than updated along with the dictionary as in the traditional cases. Moreover, a new cost function is proposed to simultaneously optimize the sensing matrix and dictionary. In order to minimize this cost function, an iterative algorithm is carried out. In every iteration, the solutions of the sensing matrix and dictionary are derived analytically. Experiments are executed with real images, especially medical images. The results demonstrate the superiority of the designed CS system composed of the optimized sensing matrix and dictionary with improved performance for image compression and reconstruction.