图像复原的Bregman迭代双正则化方法

正则化图像复原最终会导致一个大规模优化问题，提出了一种基于Bregman迭代双正则化的图像复原方法。该方法中目标函数同时考虑总变分正则化和小波域稀疏正则化，在Bregman框架下解决图像复原问题，并且给出了用于解该问题的分裂Bregman迭代算法。该算法将复杂的优化问题转化为几十次简单的迭代加以解决，每次迭代只需几次快速傅里叶变换和收缩操作即可。实验结果表明，提出的复原算法不论从客观改善信噪比还是主观视觉，都能取得很好的效果。同时与目前的复原算法相比，该算法有更快的收敛速度。

Image restoration based on Bregman iterative double regularization

To handle the large-scale optimization problem caused by regular image restoration, this paper introduces a novel image restoration method based on Bregman iterative double regularization. In this method, the designed objective function considers both the total variation regularization and the wavelet domain sparsity constraint, and solves the problem under Bregman framework with the split Bregman iterative algorithm. The algorithm converts the complex optimization problem to several iterations, each of which requires only several simple Fast Fourier Transformations and shrinkage operations. The experimental results show that the proposed method improves both the objective SNR and the subjective perceptual image quality with a faster convergence rate compared to existing approaches.