Multi-mode Core Tensor Factorization based Low-Rankness and Its Applications to Tensor Completion

TL;DR

This paper introduces a novel multi-modal core tensor factorization method with a nonconvex relaxation for low-rank tensor completion, demonstrating superior performance in applications like hyperspectral imaging, video, and MRI reconstruction.

Contribution

The paper proposes a new multi-modal core tensor factorization model with a nonconvex relaxation, improving low-rank tensor completion accuracy and efficiency.

Findings

Outperforms existing methods in hyperspectral image completion

Achieves high accuracy in MRI and video tensor completion

Efficiently models spectral low-rankness in multiple orientations

Abstract

Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex relaxation form of this measure (NC-MCTF). 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 NC-MCTF regularization minimization problem, and design an effective block successive upper-bound minimization (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.