一种新的求解低秩张量补全的随机算法

A New Stochastic Algorithm for Low-rank Tensor Completion Problems

本文针对目标函数可分离的低Tucker秩张量补全问题的核范数模型,提出了一种新的随机算法.在新算法中,每一步的迭代随机地选取张量的一种模展开进行补全,从而有效地减少了张量的全部模展开补全带来的巨大计算量,大大提高了计算效率.随后,在一定的假设条件下,证明了新算法的收敛性.最后,通过随机张量补全与图像修复的数值试验表明新算法的有效性.

In this paper,a new stochastic algorithm is proposed for solving the nuclear norm model of low-Tucker rank tensor completion problems.In the new algorithm,one mode of the tensor expansion is randomly completed in each iteration,which effectively reduces the huge computational effort caused by the completion of all modes of the tensor expansion.Then,the convergence analysis of the new algorithm is given under certain assumptions.Finally,the numerical experiments on random tensor completion problems and image restoration show the effectiveness of the proposed algorithm.