Abstract: A matching gradient distribution group based sparse representation model is researched, in which the basic unit of sparse representation is the group composed by nonlocal patches with similar structures, simultaneously the gradient histogram preserving regularization is added to match gradient distribution, and imprecise Augmented Lagrange multiplier method is used to solve the model. It is well shown by the results that this method can not only shorten the time of image processing, but also retain the fine or small-scale texture structure as well as denoising effectively, and obtain higher output PSNR and SSIM than some current state-of-the-art schemes. In case of the rich details of the image is needed, this method has practical value and realistic significance.