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Group sparse representation (GSR) is powerful for image restoration; it however often leads to undesirable sparse solutions in practice. In order to improve the quality of image restoration based on GSR, the sparsity residual model expects the representation learned from degraded images to be as close as possible to the true representation. In this article, a group residual learning based on low\u2010rank self\u2010representation is proposed to automatically estimate the true group sparse representation. It makes full use of the relation among patches and explores the subgroup structures within the same group, which makes the sparse residual model have better interpretation furthermore, results in high\u2010quality restored images. 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