基于张量链分解的低秩张量补全研究

为了进一步提高低秩张量补全性能，针对基于传统张量分解方法的张量补全问题研究中的计算复杂问题，根据张量链分解能够将高阶张量分解成一组三阶核心张量进行有效降维的特点，本文基于张量链分解的核心张量模型，采用核范数最小化方法求解，对缺失张量的低秩补全问题进行了研究，并且分别在实际图像以及合成数据上进行了算法对比实验，实验结果证明了本文方法的有效性，与目前流行的方法相比，运行速度更快、收敛性更好、补全结果也较优。

Low-Rank Tensor Completion Based on Tensor Train Decomposition

To further improve the performance of low-rank tensor completion， for the current computational complexity in the study of tensor completion based on traditional tensor decomposition methods， high-order tensors can be decomposed into a set of third-order core tensors according to tensor train decomposition. Based on the core tensor model of tensor train decomposition， this paper uses the nuclear norm minimization method to study the problem of low-rank completion of missing tensors， and algorithm comparison experiments were carried out respectively based on images and synthetic data. The experimental results prove the effectiveness of the proposed method， and compared with the current popular methods， it runs faster， has better convergence and completion results.