Research On Tensor Restoration Using Nonconvex Low-Rank Constraint

As an information carrier,visual data plays an increasingly important role in people’s daily life,such as medical diagnosis,remote sensing,security monitoring,etc.However,during the acquisition and transmission,visual data is often corrupted.Therefore,how to accurately restore corrupted visual data is an important issue in the field of computer vision.Visual data generally contains a large amount of redundant information,which implies that visual data has a strong correlation.Thus,visual data can be approximated by low-rank tensors.Inspired by this,low-rank tensor restoration is applied to restore corrupted visual data.Among them,tensor robust principal component analysis(TRPCA)and low-rank tensor completion are two important low-rank tensor restoration methods.The former can be used to remove noise from noisy visual data,and the latter can be used to estimate missing pixel values in incomplete visual data.Although these two methods have achieved good performance in visual data restoration,they have some limitations.For instance,the difference between tensor singular values is ignored,the nonlocal redundancy of visual data is not fully utilized,and the low-rank property of tensor is not accurately described.To address the aforementioned issues,we propose two new low-rank tensor restoration models,and apply them to the visual data recovery tasks.The main work of this paper is as follows:(1)We first propose a nonconvex tensor robust principal component analysis(NTRPCA)model.Unlike the traditional TRPCA,N-TRPCA can adaptively shrink the tensor singular values by different thresholds,which better preserves the important information in visual data.In addition,TRPCA assumes that the whole data tensor is of low rank.This assumption is hardly satisfied in practice for natural visual data,restricting the capability of TRPCA to recover the edges and texture details from noisy images and videos.To this end,we integrate nonlocal self-similarity into N-TRPCA,and further build a nonconvex and nonlocal TRPCA(NN-TRPCA)model.Experimental results demonstrate that the proposed NN-TRPCA outperforms some existing TRPCA methods in visual data restoration.(2)A DCT based weighted tensor Schatten p-norm(C-WTSPN)is proposed for lowrank tensor completion.C-WTSPN treats tensor singular values differently to well preserve the important information in visual data.Meanwhile,C-WTSPN uses discrete cosine transform to replace discrete Fourier transform,which can better capture the low-rankness of tensors.Besides,the visual data in practical applications often misses pixel values and is polluted by noise simultaneously.To handle this problem,we introduce a sparse term and build a DCT based robust tensor completion(CN-RTC)model.Extensive experimental results demonstrate the effectiveness of CN-RTC in visual data restoration tasks.The above models are nonconvex low-rank tensor restoration models under the tensor singular value decomposition(t-SVD)framework.They shrink tensor singular values differently by nonconvex low-rank constraints.Thus,they well preserves important information in visual data and further improves the performance of low-rank tensor restoration.Moreover,NN-TRPCA utilizes nonlocal prior to better recover the edge and texture details in visual data.CN-RTC adopts DCT as the transform in t-SVD,obtaining lower-rank tensors for visual data restoration.These two models have achieved impressive performance in visual data restoration.Their possible future extensions are discussed at the end of this paper.