Abstract

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA [4] to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) [14] and itsinduced tensor tubal rank and tensor nuclear norm. Consider that we have a 3-way tensor   such that X = L0 + S 0 , where L0 has low tubal rank and S 0 issparse. Is that possible to recover both components? In this work, we prove that under certain suitable assumptions, we can recover both the low-rank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the  , s.t. X = L + E, L,E  where   Interestingly, TRPCA involves RPCA as a special case when n3 = 1 and thus it is a simple and elegant tensor extension of RPCA. Also numerical experiments verify our theory and the application for the image denoising demonstrates the effectiveness of our method.