混合正则化模型的交替迭代原理与图像恢复  

Alternating Iterative Principle of Hybrid Regularization Model and Image Restoration

作　　者：李旭超 李玉叶[2] 

机构地区：[1]赤峰学院计算机与信息工程学院,赤峰024000 [2]赤峰学院数学与统计学院,赤峰024000

出　　处：《科学技术与工程》2017年第7期77-84,共8页Science Technology and Engineering

基　　金：国家自然科学基金(11402039);内蒙古自治区科技厅自然科学基金(2016MS0602);内蒙古自治区高等学校科学研究项目(NJZY16254)资助

摘　　要：由有界变差函数的半范数(TV)描述的正则项,在图像恢复过程中,对于图像的纹理部分,容易造成细节丢失;对于图像的卡通部分,容易产生阶梯效应;为克服此缺点,提出一种混合卡通-纹理正则化模型(hybrid cartoon texture regularization model,HCTRM)和交替迭代算法。首先,对受系统和噪声模糊的图像,用Kullback-Leibler函数描述拟合项;对于图像的卡通部分用分数阶TV的半范数来描述,纹理部分用紧框架域L_1范数来描述,建立HCTRM。其次,分析HCTRM解的存在性和唯一性。再次,引入辅助变量,将HCTRM转化为标准表达式,应用交替方向乘子算法(ADMM),将HCTRM分解为2个大的子问题。最后,将每个大的子问题,再分裂为2个小的容易处理的子问题,形成快速交替迭代算法。针对TV的半范数作为正则项,容易消除图像的纹理,且产生阶梯效应的缺点,提出一种HCTRM和交替迭代算法。仿真表明,能有效地恢复非平稳区域的纹理,克服在平稳区域产生的阶梯效应,取得较高的峰值信噪比和结构相似测度。In the processing of image restoration,regularization term is described by TV（total variation）function semi-norm,for image texture part,which easily makes image detail information vanish,for image cartoon part,which easily produces stair effects.In order to overcome the shortcomings,the proposed provides a hybrid cartoon texture regularization model（HCTRM） and alternating iterative algorithm.Firstly,for image blurred by system and noise,the fidelity term is described by Kullback-Leibler function,the cartoon part of image is described by fractional order TV semi-norm,texture part of image is described by L_1 norm,HCTRM is established.Secondly,the existence and unique properties of solution of HCTRM are analyzed.Thirdly,HCTRM is converted into standard formula by introducing auxiliary variables,and the HCTRM is decomposed into two big sub-problems by alternating direction method of multipliers（ADMM）.Finally,every big sub-problem is divided into two small and easily computational sub-problems,which form quick alternating iterative algorithm.For the shortcomings of TV semi-norm for regularization term,which easily eliminates image texture and produces stair effects,a new HCTRM and alternating iterative algorithm is proposed,simulation shows the proposed can effectively restore image texture information in non-stationary area and eliminate stair effects in stationary area,and achieve the higher peak signal to noise ratio and structural similarity index measure.

关 键 词：卡通-纹理 混合正则化模型 交替迭代 图像恢复 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]