宁夏大学第五届（数学）研究生暑期学校系列报告六
报告题目：Robust Low-Tubal-Rank Tensor Recovery from Binary Measurements
报告时间：2021年7月13日14：30—16：30
报告方式：宁夏大学怀远校区宁远楼213（线上同步腾讯会议ID 849 6729 8611）
报告内容：This talk focuses on the recovery of low-tubal-rank tensors from binary measurements based on tensor-tensor product (or t-product) and tensor Singular Value Decomposition (t-SVD). Two types of recovery models are considered, one is the tensor hard singular tube thresholding and the other one is the tensor nuclear norm minimization. In the case no random dither exists in the measurements, our research shows that the direction of tensor
with tubal rank r can be well approximated from
random Gaussian measurements. In the case nonadaptive dither exists in the measurements, it is proved that both the direction and the magnitude of
can be simultaneously recovered. As we will see, under the nonadaptive measurement scheme, the recovery errors of two reconstruction procedures decay at the rate of polynomial of the oversampling factor
(m is the random Gaussian measurements). In order to obtain faster decay rate, we introduce a recursive strategy and allow the dithers in quantization to be adaptive to previous measurements for each iterations. Under this quantization scheme, two iterative recovery algorithms are proposed which establish recovery errors decaying at the rate of exponent of the oversampling factor
. Numerical experiments on both synthetic and real-world data sets are conducted and demonstrate the validity of our theoretical results and the superiority of our algorithms.
嘉宾简介：
王建军，博士，西南大学三级教授，博士生导师，重庆市学术带头人，重庆市创新创业领军人才，巴渝学者特聘教授，重庆工业与应用数学学会副理事长，CSIAM全国大数据与人工智能专家委员会委员，美国数学评论评论员，曾获重庆市自然科学奖励。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(深度学习)逼近复杂性和高维数据稀疏建模等方面有一定的学术积累。主持国家自然科学基金5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2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22余次。已在IEEE Transactions on Pattern Analysis and Machine Intelligence（2）, IEEE Transactions on Neural Networks and Learning System（2），Applied and Computational Harmonic Analysis(2),Inverse Problems, Neural Networks, Signal Processing(2), IEEE Signal Processing letters(2), Journal of Computational and applied mathematics, ICASSP，IET Image processing(2), IET Signal processing(4),中国科学(A,F辑)(4),数学学报,计算机学报,电子学报(3)等知名专业期刊发表90余篇学术论文,IEEE等系列刊物，National Science Review及Signal Processing，Neural Networks，Pattern Recognization，中国科学,计算机学报，电子学报，数学学报等知名期刊审稿人。
联系方式：wjj@swu.edu.cn
个人网页：http://math.swu.edu.cn/s/math/index2jiaoshoutea14sub1.html
宁夏大学数学统计学院 宁夏师范学院数学与计算机科学学院
2021年7月9日
