Nonlocal robust tensor recovery with nonconvex regularization

报告人简介：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2项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）。

报告内容：The robust tensor recovery problem consists in reconstructing a tensor from a sample of entries corrupted by noise, which has attracted great interest in a wide range of practical situations such as image processing and computer vision.

In this talk, we study robust tensor recovery for third-order tensors with different degradations, which aims to recover a tensor from partial observations corrupted by Gaussian noise and sparse noise simultaneously. In contrast to traditional approaches based on the tensor nuclear norm penalty for the low-rank component and the tensor l1 norm penalty for the sparse component, we propose a nonlocal robust low-rank tensor recovery model with nonconvex regularization (NRTRM) to explore the global low-rankness and nonlocal self-similarity of the underlying tensor. The NRTRM method is first to extract similar patched-tubes to form a third-order sub-tensor. Then a class of nonconvex low-rank penalties and nonconvex sparse penalties are employed to explore the low-rank component and the sparse corruptions for such sub-tensor, respectively. Moreover, a proximal alternating linearized minimization algorithm is developed to solve the resulting model in each group and its convergence is established under very mild conditions. Extensive numerical experiments on both multispectral images and video datasets demonstrate the superior performance of NRTRM in comparison with several state-of-the-art methods.