中文摘要：

提出一种结合非局部自相似和Shearlet稀疏性正则化的图像恢复变分模型。模型采用观测图像与待恢复图像的能量误差为保真项,联合Shearlet稀疏性和非局域自相似性为混合正则化项。正则化项同时兼顾图像的变换特性和自身结构全局特性。基于变量分裂增广拉格朗日法提出了求解该变分模型的数值算法。以图像去模糊和图像修复为例,对算法性能进行了测试。实验结果表明,该模型和所提算法能够较好地恢复图像,与其他算法相比,可获得更高的峰值信噪比（PSNR）和结构自相似指标（SSIM）,具有更好的视觉效果。

英文摘要：

In this paper, a Shearlet sparsity and nonlocal self-similarity based image reconstruction model is proposed. In the new model, the energy error between the observed image and the image to be reconstructed is used as fidelity term. The Shearlet sparsity and non-local similarity are used as hybrid a regularization term, which takes into account transformation and structural characteristics of images. Furthermore, an efficient variable splitting augmented Lagrangian algorithm is developed to solve the above combined sparsity and non-local regularization constrained problem. Image deblurring and image inpaint are used as examples to test the performance of the proposed method. Experimental results show that the proposed method can preferably reconstruct the images and achieve improvement over the state-of-the-art methods in Peak-Signal-to-Noise-Ratio （PSNR） and structural similarity （SSIM） index.