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Sparse coding of images is traditionally done by cutting them into smallpatches and representing each patch individually over some dictionary given apre-determined number of nonzero coefficients to use for each patch. In lack ofa way to effectively distribute a total number (or global budget) of nonzerocoefficients across all patches, current sparse recovery algorithms distributethe global budget equally across all patches despite the wide range ofdifferences in structural complexity among them. In this work we propose a newframework for joint sparse representation and recovery of all image patchessimultaneously. We also present two novel global hard thresholding algorithms,based on the notion of variable splitting, for solving the joint sparse model.Experimentation using both synthetic and real data shows effectiveness of theproposed framework for sparse image representation and denoising tasks.Additionally, time complexity analysis of the proposed algorithms indicate highscalability of both algorithms, making them favorable to use on large megapixelimages.

Global hard thresholding algorithms for joint sparse image representation and denoising