报告题目：Singular value decomposition of Quaternion tensors and tensor completion for color video recovery

报 告 人：张立平 副教授

报告地点：腾讯会议 236 189 405

报告时间：2022年12月9日星期五9: 00-10:00

报告摘要：In this talk, by introducing an extensive quaternion discrete Fourier transformation (QDFT) based on a pure quaternion basis, we propose a novel multiplication principle for third-order quaternion tensor named gQt-product, and then a new SVD is given. With such SVD, we establish two low-rank quaternion tensor completion models to recover the incomplete color video data, and present an alternating least-squared (ALS) algorithm to solve the color video recovery problems. The numerical experiments show that our methods outperform other state-of-the-arts in the recovery accuracy and computational efficiency.

报告人简介：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, 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。