Group-based sparse representation (GSR) uses image nonlocal self-similarity (NSS) prior to grouping similar image patches, and then performs sparse representation. However, the traditional GSR model restores the image by training degraded images, which leads to the inevitable over-fitting of the data in the training model, resulting in poor image restoration results. In this paper, we propose a new hybrid sparse representation model (HSR) for image restoration. The proposed HSR model is improved in two aspects. On the one hand, the proposed HSR model exploits the NSS priors of both degraded images and external image datasets, making the model complementary in feature space and the plane. On the other hand, we introduce a joint sparse representation model to make better use of local sparsity and NSS characteristics of the images. This joint model integrates the patch-based sparse representation (PSR) model and GSR model, while retaining the advantages of the GSR model and the PSR model, so that the sparse representation model is unified. Extensive experimental results show that the proposed hybrid model outperforms several existing image recovery algorithms in both objective and subjective evaluations.

The group sparse representation (GSR) model combines local sparsity and nonlocal similarity in image processing, and achieves excellent results. However, the traditional GSR model and all subsequent improved GSR models convert the RGB space of the image to YCbCr space, and only extract the Y (luminance) channel of YCbCr space to change the color image to a gray image for processing. As a result, the image processing process cannot be loyal to each color channel, so the repair effect is not ideal. A new group sparse representation model based on multi-color channels is proposed in this paper. The model processes R, G and B color channels simultaneously when processing color images rather than processing a single color channel and then combining the results of different channels. The proposed multi-color-channels-based GSR model is compared with state-of-the-art methods. The experimental contrast results show that the proposed model is an effective method and can obtain good results in terms of objective quantitative metrics and subjective visual effects.