Reweighted Low-Rank Tensor Decomposition and its Applications in Video Denoising

A tensor is decomposed into low-rank and sparse components by simultaneously minimizing tensor nuclear norm and the $l_1$ norm in Tensor Principal Component Pursuit (TPCP). Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this paper proposes a reweighted singular value enhancement scheme to improve tensor low tubular rank in TPCP. The sparse component of a tensor is also recovered by the reweighted $l_1$ norm which enhances the accuracy of decomposition. An efficient iterative decomposition scheme based on t-SVD is proposed which improves low-rank signal recovery significantly. The effectiveness of the proposed method is established by applying to video denoising problem, and experimental results reveal that the algorithm outperforms its counterparts.