发表机构
Tongji University（同济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对t-积张量最小二乘问题，提出带重球动量的随机平均块坐标下降法，通过平均技术避免计算Moore-Penrose逆，并自适应确定步长与动量，理论证明收敛且改进线性收敛率，实验验证其迭代效率与视频恢复性能。
AI 中文摘要
针对t-积下的张量最小二乘问题，提出了一种带重球动量的张量随机平均块坐标下降法。建立了张量块坐标下降法的理论分析，并应用平均技术以避免计算张量Moore-Penrose逆。为进一步加速收敛，在块坐标下降法中引入了重球动量方案，其中步长和动量参数通过二维最小残差投影自适应确定。理论分析给出了新方法的收敛性，并提供了线性收敛率的改进界。数值实验进一步验证了所提方法在迭代次数和更好的视频恢复性能方面的效率。
英文摘要
A tensor randomized average block coordinate descent method with heavy-ball momentum is proposed for the tensor least squares problem with respect to the t-product. Theoretical analysis for tensor block coordinate descent method is established and average techniques are applied to avoid the computation of tensor Moore--Penrose inverse. To further accelerate convergence, a heavy-ball momentum scheme is incorporated into the block coordinate descent method, where the step size and momentum parameters are adaptively determined by a two-dimensional minimal residual projection. Theoretical analyses give the convergence of the new method and provide an improved bound on the linear convergence rate. Numerical experiments further verify the efficiency of the proposed method in terms of the number of iterations and the better video recovery performance.
