Tensor Robust Principal Component Analysis via Tensor Fibered Rank and lp Minimization

Tensor robust principal component analysis (TRPCA) is an important method to handle high -dimensional data and has been widely used in many areas. In this paper, we mainly focus on the TRPCA problem based on tensor fibered rank for sparse noise removal, which aims to recover the low-fib ered-rank tensor from grossly corrupted observations. Usually, the l1-norm is used as a convex approximation of tensor rank, but it is essentially biased and fails to achieve the best estimation performance. Therefore, we first propose a novel nonconvex model named TRPCAp, in which the lp norm (0 < p < 1) is adopted to approximate tensor fibered rank and measure sparsity. Then, an error bound of the estimator of TRPCAp is established and this error bound can be better than those of similar models based on Tucker rank or tubal rank. Further, we use the alternating direction method of multipliers to solve TRPCAp and provide convergence guarantee. Finally, extensive experiments on color images, videos, and hyperspectral images demonstrate the effectiveness of the proposed method.

Automated summary

This paper introduces the application of Tensor Robust Principal Component Analysis (TRPCA) in sparse noise removal. A novel nonconvex model TRPCAp is proposed and its error bound is established. The alternating direction method of multipliers is used to solve TRPCAp, and the effectiveness of the proposed method is demonstrated through extensive experiments.