基于对数全变分极小化的张量补全  

Tensor Completion Based on Logarithmic Total Variation Minimization

作　　者：卢丹 王建军[1] Lu Dan;Wang Jianjun(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆北碚400715

出　　处：《宁夏大学学报（自然科学版）》2024年第1期1-8,共8页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12071380)。

摘　　要：在张量补全问题中,低秩性与局部光滑性是被高频使用的先验信息,因此有许多与其相关的研究.而且为了更精确地恢复图像,低秩性正则与编码局部光滑性的全变分正则往往会被以简单加权组合的方式引入相关模型.但许多真实图像往往同时具有低秩性与局部光滑性先验信息.此外,在这些模型中张量核范数常被用于挖掘低秩性先验,但它平均地缩小所有奇异值,从而不能很好地保留图像信息.为此,提出了张量对数相关全变分(TLOGCTV)正则,其中使用了张量对数范数而不是核范数,从而更好地挖掘低秩先验信息,同时,使用全变分刻画局部光滑性先验信息.而且相较于简单加权组合方式引入正则的模型,所提出的模型仅需要一个平衡参数.随后基于该正则项建立了相应的张量补全模型,并且给出该模型的优化求解算法.在多光谱与高光谱上的一系列实验验证了模型的有效性.Low rankness and local smoothness priors are frequently used in tensor completion problems.And there are many works related to them.In order to better and accurately restore the image,the low rankness regularization and total variation regularization encoding local smoothness are often introduced into the correlation model in the form of a simple weighted combination.However,many real-world images tend to have low rankness and local smoothness priors.In addition,in these models,the tensor nuclear norm is often used to mine the low-rank prior.However,it does not retain the image information well since it reduces all singular values evenly.To this end,this paper proposes a tensor logarithmic correlated total variation regular(TLOGCTV),in which the tensor logarithmic norm is used instead of the nuclear norm to better mine the low-rank prior,and the total variation is used to characterize the smoothness prior.Moreover,compared with the model that introduces regular terms in a simple weighted combination,the proposed model only needs one balance parameter.Subsequently,based on the regular term,the corresponding tensor completion model is established,and the optimization algorithm of the model is given.A series of experiments on multi-spectral and hyper-spectral images have demonstrated the superiority of the regular model compared with other models.

关 键 词：张量补全 张量对数范数 非凸全变分 

分 类 号：TP399[自动化与计算机技术—计算机应用技术]