Adaptive Singular Value Shrinkage For Low Rank Tensor Denoising

In this work,we consider low rank tensor denoising problem.Tensors are widely used to represent high dimensional data with internal spatial or temporal relations,e.g.,images,videos,hyperspectral images.Traditional tensor decomposition models,such as CP decomposition and Tucker decomposition,treat every mode of tensors equally.However,in real applications,some modes act differently from other modes,e.g.,chan-nel mode of images,time mode of videos,wave mode of hyperspectral images.The recently proposed model called t-SVD aims to tackle with such problems.Based on the t-SVD decomposition,we use different shrink functions to shrink the tensor singular values,in order to obtain low rank estimators of true signals.In addition,we derive the Stein's unbiased risk estimate(SURE)of the proposed estimators.With the help of SURE,we establish adaptive tuning parameter selection procedure by minimizing the SURE criterion.More specifically,the parameter selection procedure is totally data driven and simultaneous with the estimation process.The whole modeling procedure requires only one round of t-SVD.We conduct experiments on simulation data,images,videos,and hyperspectral data.The results show that the proposed SURE approximates the true risk function accurately.Moreover,the proposed model selection procedure picks good tuning parameters out.We show the superiority of our model by compar-ing with state-of-the-art denoising models.The experiments manifest that our model outperforms in both quantitive metrics(e.g.,RSE,PSNR)and visualizing results.