Robust Tensor Completion Using Transformed Tensor SVD

Tensor (multidimensional arrays) are generalizations of vectors and matrices, which can be used as a powerful tool in modeling multidimensional data such as videos [29], color images [36, 40], hyperspectral images [11, 35, 49], and electroencephalography (EEG) [8]. Based on its multilinear algebraic properties, a tensor can take full advantage of its structures to provide better understanding and higher accuracy of the multidimensional data. In many tensor data applications [9, 20, 27, 33, 37, 40, 41, 47, 50], tensor data sets are often corrupted and/or incomplete owing to various unpredictable or unavoidable situations. It is motivated us to perform tensor completion and tensor robust principal component analysis for multidimensional data processing. Compared with matrix completion and robust principal component analysis, tensor completion and tensor robust principal component analysis are far from being well-studied. The main issues are the definitions of tensor ranks and tensor decompositions.