Low-rank tensor train for tensor robust principal component analysis

Abstract Recently, tensor train rank, defined by a well-balanced matricization scheme, has been shown the powerful capacity to capture the hidden correlations among different modes of a tensor, leading to great success in tensor completion problem. Most of the high-dimensional data in the real world are more likely to be grossly corrupted with sparse noise. In this paper, based on tensor train rank, we consider a new model for tensor robust principal component analysis which aims to recover a low-rank tensor corrupted by sparse noise. The alternating direction method of multipliers algorithm is developed to solve the proposed model. A tensor augmentation tool called ket augmentation is used to convert lower-order tensors to higher-order tensors to enhance the performance of our method. Experiments of simulated data show the superiority of the proposed method in terms of PSNR and SSIM values. Moreover, experiments of the real rain streaks removal and the real stripe noise removal also illustrate the effectiveness of the proposed method.