报告题目：Robust Low-Rank Tensor Completion via Transformed Tensor Nuclear Norm with Total Variation Regularization

报告人：白敏茹 教授

报告摘要：Robust low-rank tensor completion plays an important role in multidimensional data ****ysis against different degradations, such as Gaussian noise, sparse noise, and missing entries, and has a variety of applications in image processing and computer vision. In this paper, we investigate the problem of low-rank tensor completion with different degradations for third-order tensors, and propose a transformed tensor nuclear norm method combined the tensor $\ell_1$ norm with total variational (TV) regularization. Our model is based on a recently proposed algebraic framework in which the transformed tensor nuclear norm is introduced to capture lower transformed multi-rank by using suitable unitary transformations. We adopt the tensor $\ell_1$ norm to detect the sparse noise, and the TV regularization to preserve the piecewise smooth structure along the spatial and tubal dimensions. Moreover, a symmetric Gauss-Seidel based alternating direction method of multipliers is developed to solve the resulting model and its global convergence is established under very mild conditions. Extensive numerical examples on both hyperspectral images and video datasets are carried out to demonstrate the superiority of the proposed model compared with several existing state-of-the-art methods.

报告人简介：白敏茹，湖南大学数学学院教授，博士生导师，担任湖南省运筹学会副理事长、湖南省计算数学与应用软件学会副理事长、中国运筹学会数学优化学会理事，长期致力于最优化理论、方法及其应用研究，近年来主要从事张量优化、低秩稀疏优化及其在图像处理中的应用研究，主持国家自然科学基金面上项目和湖南省自然科学基金等项目，取得了系列研究成果，在SIAM Journal on Imaging Sciences、Inverse Problems, Journal of Optimization Theory and Applications, Computational Optimization and Applications, Journal of Global Optimization等学术期刊上发表论文近30余篇，获得2017年湖南省自然科学二等奖（排名第二）。

报告时间：2020年12月10日，周四，下午14：30--15：30

报告地点：腾讯会议 985 7643 4402

学院联系人：胡胜龙