Online Learning Sensing Matrix and Sparsifying Dictionary Simultaneously for Compressive Sensing

This paper considers simultaneously optimizing the Sensing Matrix and Sparsifying Dictionary (SMSD) on a large training dataset. 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 optimizing the sparsifying dictionary on a large training dataset when the sensing matrix is fixed. Benefiting from training on a large dataset, the obtained compressive sensing system via 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 and efficiency of the proposed online algorithm compared with the existing methods.