Alternating Optimization of Sensing Matrix and Sparsifying Dictionary for Compressed Sensing

This paper deals with alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing systems. Under the same framework proposed by J. M. Duarte-Carvajalino and G. Sapiro, a novel algorithm for optimal sparsifying dictionary design is derived with an optimized sensing matrix embedded. A closed-form solution to the optimal dictionary design problem is obtained. A new measure is proposed for optimizing sensing matrix and an algorithm is developed for solving the corresponding optimization problem. Experiments are carried out with synthetic data and real images, which demonstrate promising performance of the proposed algorithms and superiority of the CS system designed with the optimized sensing matrix and dictionary to existing ones in terms of signal reconstruction accuracy. Particularly, the proposed CS system yields in general a much improved performance than those designed using previous methods in terms of peak signal-to-noise ratio for the application to image compression.