报告名称：Singular Value Decomposition of Third Order Quaternion Tensors and Applications in Color Video impaiting

主讲人：张立平 副教授

邀请人：莫长鑫 讲师

时间：2022年5月23日   14:30

地点：腾讯会议（ID：484 506 041）

主办单位：数学科学学院

报告摘要

A novel tensor product for third order quaternion tensors is proposed. With this tensor product, we further define the singular value decomposition and the rank of a third order quaternion tensor. It is also proved that the best rank-k approximation of a third order quaternion tensor exists. On the other hand, note that a color video can be expressed as a third order quaternion tensor, the proposed singular value decomposition thus opens up a new way to analyze the structure of color video. Finally, some experiments are performed to demonstrate the low-rankness of color videos. We propose a novel low rank quaternion tensor completion model for color video inpainting. The convergence and convergence rate are established. The numerical experiments on color videos demonstrate the superior performance and efficiency of our method over state-of-the-arts methods.

专家简介

张立平，清华大学长聘副教授，博士生导师，研究方向最优化理论算法及应用，在求解互补与变分不等式问题、半无限规划、张量优化等方面取得了一些有意义的结果。已在Mathematics of Computation, SIAM Journal of Matrix Analysis and Applications, SIAM Journal on Optimization, Applied Numerical Mathematics，中国科学等期刊发表高质量论文五十余篇、连续获得多项国家自然科学基金资助。曾获得教育部自然科学奖二等奖和北京市科学技术奖二等奖。