应用双稀疏模型和ADMM优化的图像复原

基于稀疏表示的图像复原算法大都只利用了图像整体稀疏性和局部稀疏性中的一种，未充分利用图像的先验知识，基于此，本文在稀疏表示框架下，同时引入Cosparse解析模型及平移不变小波变换两种稀疏模型，前者对每个图像块进行稀疏表示，后者对整幅图像进行稀疏表示，从而提出一种新的图像复原算法。该算法将图像复原问题归结为双稀疏正则化问题。为求解复杂的双稀疏优化问题，本文运用交替方向乘子法 (ADMM, Alternating Direction Method of Multipliers)算法将该约束优化问题分解为若干子问题，通过交替迭代求解获得复原图像。实验中对不同类型的模糊图像进行了复原，其结果表明该算法对于各类模糊图像的复原比现有复原算法效果更好，从而验证了算法的有效性。 

Image Restoration based on Double Sparse Model and ADMM Optimization

Image restoration algorithms based on sparse representation generally use the whole sparsity or the local sparsity of the image, while not make full use of prior knowledge of the image. Based on this, in the framework of sparse representation, this article proposed a new image restoration algorithm introducing both the Cosparse analysis model leading to a sparse representation of each image patch and translation invariant wavelet transform leading to a sparse representation over the whole image. In the algorithm, the problem of image restoration is expressed as the double sparse regularization problem. To solve the complex double sparse optimization problem, the alternating direction method of multipliers is introduced to decompose the issue into equivalent sub-problems. By alternatively and iteratively solving the sub-problems, the restored image is obtained. In the experiments, the images blurred by different type of blur are restored. The experimental results show that, the proposed algorithm outperforms the existing restoration algorithms. Thus, the effectiveness of the proposed algorithm is verified.