变量分裂机制耦合非循环模糊模型的图像复原

Image Restoration Based on Variable Splitting Coupled Non-Circulant Blurring Model

目的针对当前非二次正则化图像复原算法在图像边界的周期拓展难度较大,导致复原图像的边界存在振铃效应,算法的通用性削弱,且时耗严重的问题,提出变量分裂机制耦合非循环卷积模型的抗失真图像快速复原算法。方法引入掩模算子,设计非循环模糊模型,显著消除复原图像的振铃效应;改进数据保真项,构造了最小成本化函数;定义二次辅助变量,嵌入变量分裂策略,设计基于变量分裂的乘数交替方向算法,对非循环模糊模型中的循环与掩模矩阵进行解耦,降低算法复杂度;构造增广拉格朗日函数,耦合交替最小机制与成本函数,以单步封闭式更新估算图像,快速完成图像重构。结果仿真结果显示:与当前复原算法相比,提出算法的失真度最小,且收敛速度更快。结论提出算法能够快速复原多种类型的退化图像,有效消除了复原图像的振铃效应。

In order to solve the defects such as ringing effect on boundary of image restoration and weakening of the generality and seriously time consuming of current non-quadratic regularization image restoration algorithm, the anti-distortion and fast image restoration algorithm based on the variable splitting coupled non-circulant blurring model was proposed in this paper. The non-circulant blur model was designed by introducing the mask operator to effectively eleminate the ring effects; and the minimizing cost function was constructed by improving the data fidelity term; then the multiplier alternating direction algorithm was designed by embedding the variable splitting and defining the second auxiliary variable to decouple the circular matrix and the mask matrix of non-circular bluring model to reduce the complexity of this algorithm. Finally, the degraded image was fastly restorated by single-step closed-form updation of the estimation of image based on constrcuting the augmented Lagrange function, and coupling alternating leastmechanism as well as cost function.Simulation results showed that compared with the current image restoration algorithm, the distortion of this algorirhm was smaller; and its convergence speed was faster. This proposed algorithm can fast resrotate multiple types of degraded images,and effectively eleminated the ringing effect of restorated images.