Abstract: This paper studies the tensor completion problem based on Tucker rank for high-dimensional data whose entries are prone to missing during acquisition, transmission, and storage. To alleviate the over-penalization of large singular values caused by nuclear norm relaxation and improve the solution efficiency of the difference-of-convex model, an inertial Bregman proximal difference-of-convex algorithm is proposed within the proximal difference-of-convex algorithm framework. The proposed algorithm introduces an inertial extrapolation strategy and replaces the traditional Frobenius norm proximal term with a Bregman-distance-induced proximal term, thereby characterizing the structural information of tensor completion problems more flexibly. On the theoretical side, under a suitable compactness assumption on the level set and the Kurdyka-Łojasiewicz property, the convergence of the sequence generated by the algorithm is proved, and its limit points are shown to be stationary points of the corresponding optimization model. Experiments on brain MRI image recovery show that, compared with the proximal difference-of-convex algorithm, the proposed algorithm achieves higher recovery accuracy; compared with the high-accuracy low-rank tensor completion algorithm, the proposed algorithm has an advantage in computation time.

Key words: tensor completion, Tucker rank, DC model, Bregman distance, proximal gradient algorithm