应兰州大学数学与统计学院李朋副教授邀请,西南大学数学与统计学
院王建军教授,将于2022年4月14日(周四)上午9：00在线举办专题报告.
报告题目：Low Tubal Rank Tensor Sensing and Robust PCA from Quantized Measurements
报告时间：2021年4月14日(星期四)上午9：00
腾讯会议ID：488-124-877
报告摘要：Low-rank tensor Sensing (LRTS) is a natural extension of low-rank matrix Sensing (LRMS) to high-dimensional arrays, which aims to reconstruct an underlying tensor X from incomplete linear measurements M(X). However, LRTS ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of M(X). We still hope to recover X from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed---the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real n1*n2*n3tensor X with tubal rank r from m random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor lambda:=m/((n_1+n_2)n_3r). To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of lambda. Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.
Quantized Tensor Robust Principal Component Analysis (Q-TRPCA) aims to recover a low-rank tensor and a sparse tensor from noisy, quantized, and sparsely corrupted measurements. A nonconvex constrained maximum likelihood (ML) estimation method is proposed for Q-TRPCA. We provide an upper bound on the Frobenius norm of tensor estimation error under this method. Making use of tools in information theory, we derive a theoretical lower bound on the best achievable estimation error from unquantizedmeasurements. Compared with the lower bound, the upper bound on the estimation error is nearly order-optimal. We further develop an efficient convex ML estimation scheme for Q-TRPCA based on the tensor nuclear norm (TNN) constraint. This method is more robust to sparse noises than the latter nonconvex ML estimation approach. Conducting experiments on both synthetic data and real-world data, we show the effectiveness of the proposed methods.
报告人简介
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,重庆市运筹学会副理事长, 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. 他已在IEEE PAMI(2),IEEE TNNLS(2)，Appl. Comput. Harmonic Anal.(2), Inverse Problems, Neural Networks, Signal Process(2),IEEE Signal Process Letter(2),J. Comput. Appl. Math.,ICASSP,IET Image Process.(2), IET Signal Process.(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. 王建军教授担任IEEE等系列物National Science Review., Signal Process., Neural Network. Pattern. Recognition., 中国科学，计算机学报，电子学报，数学学报等知名刊物的审稿人.
甘肃应用数学中心
甘肃省高校应用数学与复杂系统省级重点实验室
数学与统计学院
萃英学院
2022年4月12日
