Abstract: The most existing denoising algorithms based on nonlocal sparse representation are strictly dependent on patch matching, and the denoising performance is subject to the numbers of similar patches. So a image denoising algorithm based on nonlocally sparse representation and group is proposed. The group-based constraints is introduced to the nonlocal sparse representation, which can enhance the nonlocal similarity between image patches and the patch matching is more accurate. Experiments show that the model has a good performance in both visual effect and peak signal to noise ratio.