基于Tikhonov正则的图像盲复原算法  

Blind Image Restoration Algorithm Based on Tikhonov Regularization

作　　者：杨天骥 姜亚琴[1] 郭小亚 YANG Tian-ji;JIANG Ya-qin;GUO Xiao-ya(School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《计算机技术与发展》2022年第5期29-35,共7页Computer Technology and Development

基　　金：国家自然科学基金面上项目(11671004)。

摘　　要：图像在获取、传输及保存的过程中,很多因素会导致图像质量退化,图像模糊是图像质量退化的一种常见表现。基于全变差(TV)的图像复原Chan模型虽然能较好地刻画导致图像质量退化的模糊核,但该模型的图像复原结果严重依赖于参数的选取。针对Chan模型对参数敏感的问题,在该模型中引入模糊核的Tikhonov正则,提出新的盲去糊模型,并证明新的盲复原模型解的存在性。另外,采用由粗到精的多层图像金字塔策略,构造模糊核的初始值,再结合交替极小化(alternating minimization,AM)方法,设计基于初始模糊核的快速算法求解所提模型。数值实验结果表明:所提模型与其他正则化模型相比,在不需要模糊核动态阈值约束的前提下,不仅能得到高质量的图像复原结果,而且对参数有较好的鲁棒性。Image degradation is influenced by many factors during image acquisition,transmission and preservation.Image blur is a common representation of image degradation.Blur kernel leads to the degradation of image quality.Although the Chan model based on total variation(TV)can estimate the blur kernel,the restoration result of this model depends heavily on the selection of parameters.In this paper,a new blind image deblurring model is proposed by introducing the Tikhonov regularization into Chan model in order to overcome the effect of parameter sensitivity.Then,the existence of solution of the new blind restoration model is proved.Besides,the initial value of the blur kernel is constructed using a multi-layer image pyramid strategy from coarse to fine and a fast algorithm based on the initial blur kernel is designed combining alternating minimization(AM)method for solving the proposed model numerically.On the premise of without the constraint of blur kernel dynamic threshold,numerical results show that the proposed model can not only get high quality image restoration results,but also has stronger robustness for parameters compared with other regularization models.

关 键 词：变分法 盲复原 金字塔策略 吉洪诺夫正则 交替迭代极小化 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]