关于举行黄正海教授（天津大学）学术报告会的通知

报告题目: Tensor Robust Principal Component Analysis via Tensor Fibered Rank and Lp Minimization  

报 告人: 黄正海教授

报告时间: 2022年8月18日（星期四）上午9:30-11:30              

报告地点： 腾讯会议号：853-345-092  会议密码：220818

https://meeting.tencent.com/dm/G24z4wnBHasB

邀 请人: 潘少华 教授

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数学学院

2022年8月15日

报告摘要：Tensor Robust Principal Component Analysis (TRPCA) is an important method to handle high-dimensional data and has been widely used in many areas. In this paper, we mainly focus on the TRPCA problem based on tensor fibered rank for sparse noise removal, which aims to recover the low-fibered-rank tensor from grossly corrupted observations. Usually, the L1-norm is used as a convex approximation of tensor rank, but it is essentially biased and fails to achieve the best estimation performance. Therefore, we first propose a novel nonconvex model named as TRPCAp, in which the Lp penalty is adopted to approximate tensor fibered rank and measure sparsity. Then, an error bound of the estimator of TRPCA Lp is established and this error bound can be better than those of similar models based on Tucker rank or tubal rank. Further, we present an efficient algorithm based on alternating direction method of multipliers to solve TRPCAp and provide convergence guarantee for this algorithm. Finally, extensive experiments on color images, videos and hyperspectral images demonstrate the effectiveness of the proposed method.  

专家简介：黄正海，天津大学数学学院教授、博士生导师。主要从事最优化理论、算法及其应用方面的研究工作，在求解互补与变分不等式问题、对称锥优化与对称锥互补问题、稀疏优化、张量优化、核磁共振医学成像、人脸识别等方面取得了一系列有意义的成果。目前的主要研究兴趣是张量优化、特殊结构的变分不等式与互补问题、以及机器学习中的优化理论方法及其应用。已发表SCI检索论文120多篇、连续获得多项国家自然科学基金资助。曾获得中科院优秀博士后奖和教育部高等学校自然科学奖二等奖。目前为中国运筹学会常务理事；国际期刊《Pacific Journal of Optimization》、《Applied Mathematics and Computation》、《Asia-Pacific Journal of Operational Research》和《Optimization,Statistics & Information Computing》的编委、中国核心期刊《运筹学学报》的编委。