Online learning sensing matrix and sparsifying dictionary simultaneously for compressive sensing

This paper considers the problem of simultaneously learning the Sensing Matrix and Sparsifying Dictionary (SMSD) on a large training dataset. To address the formulated joint learning problem, we propose an online algorithm that consists of a closed-form solution for optimizing the sensing matrix with a fixed sparsifying dictionary and a stochastic method for learning the sparsifying dictionary on a large dataset when the sensing matrix is given. Benefiting from training on a large dataset, the obtained compressive sensing (CS) system by the proposed algorithm yields a much better performance in terms of signal recovery accuracy than the existing ones. The simulation results on natural images demonstrate the effectiveness of the suggested online algorithm compared with the existing methods.