Tensor Completion Based on Logarithmic Total Variation Minimization
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 regu-larization 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 rank-ness 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 regu-lar terms in a simple weighted combination,the proposed model only needs one balance parameter.Subse-quently,based on the regular term,the corresponding tensor completion model is established,and the optimiza-tion 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.
tensor completiontensor logarithmic normnon-convex total variation
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