Online Simultaneous Learning Projection Matrix and Sparsifying Dictionary

An online algorithm is proposed in this letter to optimize the Projection Matrix and Sparsifying Dictionary (PMSD) simultaneously on a large training dataset. A closed-form solution is derived for optimizing the projection matrix with a fixed sparsifying dictionary and the stochastic method is used to optimize the sparsifying dictionary with a fixed optimized projection matrix on a large training dataset to form the proposed online algorithm. Benefiting from training on a large dataset, 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 its effectiveness and efficiency compared with the existing methods.