题目：Low-tubal-rank Tensor Analysis: Theory, Algorithms and Applications

时间：12月21日 15:00-16:00

地点：工商楼200-9

报告人：王建军（西南大学）

摘要：This talk will share our two recent results on low-tubal-rank tensor analysis. (1) LRTR: we establish a regularized tensor nuclear norm minimization (RTNNM) model for low-tubal-rank tensor recovery (LRTR). Then, we initiatively define a novel tensor restricted isometry property (t-RIP) based on tensor singular value decomposition (t-SVD). Besides, our theoretical results show that any third-order tensor whose tubal rank is at most can stably be recovered from its as few as measurements with a bounded noise constraint via the RTNNM model, if the linear map obeys t-RIP with for certain fixed . (2) TRPCA: by incorporating prior information including the column and row space knowledge, we investigate the tensor robust principal component analysis (TRPCA) problem based on t-SVD. We establish sufficient conditions to ensure that under significantly weaker incoherence assumptions than tensor principal components pursuit method (TPCP), our proposed Modified-TPCP solution perfectly recovers the low-tubal-rank and the sparse components with high probability, provided that the available prior subspace information is accurate. In addition, we present an efficient algorithm by modifying the alternating direction method of multipliers (ADMM) to solve the Modified-TPCP program. Numerical experiments show that the Modified-TPCP based on prior subspace information does allow us to recover under weaker conditions than TPCP. The application of color video and face denoising task suggests the superiority of the proposed method over the existing state-of-the-art methods.

报告人简介：王建军，教授（研究员），博士生导师，重庆市学术技术带头人，重庆市英才计划·创新领军人才， 巴渝学者特聘教授，CSIAM全国大数据与人工智能专家委员会委员，重庆市工业与应用数学学会副理事长，美国数学评论评论员，重庆数学会理事，重庆市统计学重点学科学术带头人，西南大学统计学博士一级学科负责人，以第一完成人申报的阶段性成果《复杂结构性高维数据稀疏建模的方法与算法应用》荣获重庆市自然科学三等奖，西南大学人工智能学院副院长。主要研究方向为：高维数据建模、机器学习（深度学习）、数据挖掘、压缩感知、张量分析、函数逼近论等。在神经网络逼近复杂性和稀疏逼近等方面有一定的学术积累。已在Neural Networks, Applied and Computational Harmonic Analysis, Signal Processing等专业期刊发表80余篇学术论文。主持并完成国家自然科学基金4项，教育部科学技术重点项目1项，重庆市自然科学基金1项，主研8项国家自然、社会科学基金；现主持国家自然科学基金面上项目一项，参与国家重点基础研究发展‘973’计划一项， 多次出席国际、国内重要学术会议，并应邀做大会特邀报告20余次。

联系人：郭正初（guozhengchu@zju.edu.cn）