Online Learning Sensing Matrix and Sparsifying Dictionary Simultaneously for Compressive Sensing

摘要

This paper considers simultaneously optimizing the Sensing Matrix andSparsifying Dictionary (SMSD) on a large training dataset. We propose an onlinealgorithm that consists of a closed-form solution for optimizing the sensingmatrix with a fixed sparsifying dictionary and a stochastic method foroptimizing the sparsifying dictionary on a large training dataset when thesensing matrix is fixed. Benefiting from training on a large dataset, theobtained compressive sensing system via the proposed algorithm yields a muchbetter performance in terms of signal recovery accuracy than the existing ones.The simulation results on natural images demonstrate the effectiveness andefficiency of the proposed online algorithm compared with the existing methods.