We propose a blind image deblurring model based on the group sparse representation (GSR) prior. The motivation for this work is that adjacent similar patches of images and blur kernels favor clear images and ground-truth kernels over blurred images and poor kernels. Therefore, we impose GSR constraints on similar patches based on images and kernels to ensure the sparsity of the intermediate latent images and kernels. In addition, to effectively preserve the main edges in the image, we impose an $L_0$-regularized gradient prior on image restoration. Moreover, a flexible non-convex weighted $L_p$-norm minimization is applied to the GSR and an adaptive dictionary is used for each similar group. To optimize our model, an effective optimization algorithm based on a generalized soft-thresholding algorithm and half-quadratic splitting strategy is developed. Several analyses verify the validity of the GSR prior. Experiments show that our method achieves satisfactory deblurring effects in several specific domains and is robust in both deblurring and denoising tasks. The results of qualitative and quantitative experiments indicate that our algorithm performs favorably with respect to state-of-the-art algorithms.

我们提出基于组稀疏表示（GSR）的盲图像去模糊模型。进行这项工作的动机是，相邻的相似图像块和模糊内核比模糊图像和不良内核更喜欢清晰的图像和真实的内核。因此，我们基于图像和内核对相似的补丁施加GSR约束，以确保中间潜像和内核的稀疏性。此外，为了有效保留图像中的主要边缘，我们强加了${\mathrm{大号}}_0$-图像恢复之前的正则化梯度。此外，灵活的非凸加权${\mathrm{大号}}_p$-norm最小化应用于GSR，自适应字典用于每个相似的组。为了优化我们的模型，开发了一种基于广义软阈值算法和半二次分裂策略的有效优化算法。多项分析证明了GSR的有效性。实验表明，我们的方法在几个特定的​​领域中均实现了令人满意的去模糊效果，并且在去模糊和去噪任务方面均十分可靠。定性和定量实验的结果表明，相对于最新算法，我们的算法性能良好。