Missing Information Reconstruction Of Three-Order Tensor

In recent years, researches to decompose and complete tensor have been more prosperous in many applications as theories of estimating the tensor rank arc sophisticated increasingly. The sum of nuclear norms (SNN) minimization method, which is regarded as the hest convex approximation of the Tucker-rank, seems to be successfully applied to actual computations. In state-of-the-art researches, decomposing the original tensor into a core tensor multiplied by factor matrices can lessen calculative burden of SVDs. What's more, accuracy can be improved by using the logDet function to replace the nuclear norm. To combine these advantages, we propose a core tensor logDet function minimization model which consists decomposition of the original tensor and the logDet function. Alternating direction method of multipliers (ADMIVI) is developed to solve the problem. In order to accelerate the computation speed with a convergence guarantee, a rank-adjustment strategy is utilized. Finally, experimental results have verified that our method improves the computational efficiency for large-scale problems.