基于共轭梯度法和全变差正则化的图像复原  

Image Restoration Based on Total Variation Regularization with Conjugate Gradient Method

作　　者：张彬[1] 孙菁聪 王胜文 ZHANG Bin;SUN Jing-cong;WANG Sheng-wen(School of Science,Communication University of China,Beijing 100024,China)

机构地区：[1]中国传媒大学理学院,北京100024

出　　处：《中国传媒大学学报（自然科学版）》2018年第6期14-18,共5页Journal of Communication University of China：Science and Technology

摘　　要：当图像边界满足齐性Dirichlet条件时,正则化图像复原问题可归结为求解系数矩阵为含有正则化参数的线性方程组。为了更好地复原退化图像的边缘细节,选取原图像的全变差函数为正则化函数,取定适当的正则化参数,用共轭梯度法求解线性方程组而得到复原图像。仿真结果表明:与Tikhonov正则化复原方法相比较,全变差约束能更好地保留图像的细节,对模糊图像能够取得比较满意的复原效果。从GMG和LS两种客观指标也说明了这一点。When the image boundary satisfy the homogeneous Dirichlet condition,regularized image restoration can be attributed to solving a linear systems.In order to better restore the edge details of degraded image,the total variation of original image was selected as the regularization function.The regularization parameter was selected appropriately and the linear systems was solved with conjugate gradient method to get the restoration image.Simulation results show that total variation regularization method can restored the edges and details of image better than Tikhonov regularization method.Two objective indicators from GMG and LS also illustrates this point.

关 键 词：图像复原 全变差 共轭梯度法 分块Toeplitz矩阵 

分 类 号：TP39141[自动化与计算机技术—计算机应用技术]