Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a kind of multi-modal core tensor factorization (MCTF) method together with a tensor low-rankness measure and a better nonconvex relaxation form of it (NonMCTF). The proposed models encode low-rank insights for general tensors provided by Tucker and T-SVD, and thus are expected to simultaneously model spectral low-rankness in multiple orientations and accurately restore the data of intrinsic low-rank structure based on few observed entries. Furthermore, we study the MCTF and NonMCTF regularization minimization problem, and design an effective BSUM algorithm to solve them. This efficient solver can extend MCTF to various tasks, such as tensor completion. A series of experiments, including hyperspectral image (HSI), video and MRI completion, confirm the superior performance of the proposed method.
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