Enhanced Tensor RPCA and its Application

Despite the promising results, tensor robust principal component analysis (TRPCA), which aims to recover underlying low-rank structure of clean tensor data corrupted with noise/outliers by shrinking all singular values equally, cannot well preserve the salient content of image. The major reason is that, in real applications, there is a salient difference information between all singular values of a tensor image, and the larger singular values are generally associated with some salient parts in the image. Thus, the singular values should be treated differently. Inspired by this observation, we investigate whether there is a better alternative solution when using tensor rank minimization. In this paper, we develop an enhanced TRPCA (ETRPCA) which explicitly considers the salient difference information between singular values of tensor data by the weighted tensor Schatten p-norm minimization, and then propose an efficient algorithm, which has a good convergence, to solve ETRPCA. Extensive experimental results reveal that the proposed method ETRPCA is superior to several state-of-the-art variant RPCA methods in terms of performance.