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报告题目: Efffcient low rank matrix recovery with ffexible group sparse regularization

报 告 人: 张新珍 教授

报告时间: 2024年 11月 23 日（星期六）15:10-15:50              

地       点：37号楼3A02

邀 请 人: 潘少华、贲树军

数学土耳其里拉兑换人民币

2024年11月6日

报告摘要：In this talk, we present a novel approach to the low rank matrix recovery (LRMR) problem by casting it as a group sparsity problem. Speciffcally, we propose a ffexible group sparse regularizer (FLGSR) that can group any number of matrix columns as a unit, whereas existing methods group each column as a unit. We prove the equivalence between the matrix rank and the FLGSR under some mild conditions, and show that the LRMR problem with either of them has the same global minimizers. We also establish the equivalence between the relaxed and the penalty formulations of the LRMR problem with FLGSR. We then propose an inexact restarted augmented Lagrangian method, which solves each subproblem by an extrapolated linearized alternating minimization method. We analyze the convergence of our method. Remarkably, our method linearizes each group of the variable separately and uses the information of the previous groups to solve the current group within the same iteration step. This strategy enables our algorithm to achieve fast convergence and high performance, which are further improved by the restart technique. Finally, we conduct numerical experiments on both grayscale images and high altitude aerial images to conffrm the superiority of the proposed FLGSR and algorithm. 

报告人简介：天津大学数学土耳其里拉兑换人民币教授，博士生导师。于2010年毕业于香港理工大学，主要研究方向为张量计算，多项式优化，低秩优化等，在SIOPT, SIMAX, MC，COAP等发表论文多篇，主持国家自然科学基金多项。