基于分裂 Bregman 方法的全变差图像去模糊

摘要

针对全变差图像去模糊问题,提出一种基于分裂Bregman方法的全变差图像去模糊算法,利用分裂Bregman方法来优化其求解问题模型.首先,利用辅助变量及其二次惩罚泛函把全变差去模糊优化问题转化为一个等价的无约束优化问题；其次,基于Bregman迭代将其分解为两个子优化问题采用交替最小化方法进行求解；最后,根据子问题结构特点,采用离散傅立叶变换及收缩技术实现子优化问题的快速计算.实验结果表明,在不同尺寸模糊核条件下本文算法能获得有效、稳定的图像复原结果,相比FTVd、IRN去模糊方法,本文算法复原效果更好,计算更加快速.%For total variant image deblurring problem, it was proposed a total variant image deblurring algorithm based on split bregman method, which applied split bregman method to optimizing and solving the problem model.Firstly, taken advantage of auxiliary variable and quadratic penalty function, total variant image deblurring optimization problem was converted into a uncon-straint optimization problem. Secondly,based on Bregman iterative,the problem was divided into two sub-problems and use the alternative minimization method to solving. Thirdly,according to the characteristic of subproblem structure,the Discrete Fourier Transform and Shrinkage technologies were used to implement the fast computation of sub-problems. The experimental results indicate that with different size blurry kernels, our algorithm can recover image effectively and steadily. Furthermore, compraring with FTVd and IRN deblurring methods,our algorithm can obtain better recovery results,and compute faster.