报告题目：Low tubal rank tensor sensing and robust PCA from quantized measurements

报告人：西南大学数学与统计学院王建军教授

报告时间：2023年4月19日 19:30-20:30

报告地点：腾讯会议700-736-7496

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.Under the tensor Singular Value Decomposition (t-SVD) framework,two recovery methods are proposed.These methods can recover a real tensor X with tubal rank r from m random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor.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.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 unquantized measurements.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.Numerical experiments verify our results,and the applications to real-world data demonstrate the promising performance of the proposed methods. 

报告人简介：

王建军，博士，西南大学数学与统计学院教授，博士生导师，重庆市学术技术带头人，巴渝学者特聘教授，重庆市工业与应用数学学会副理事长，重庆市运筹学会副理事长，美国数学评论评论员，重庆数学会常务理事，曾获重庆市自然科学奖，主要研究方向为：高维数据建模、压缩感知、低秩张量分析、神经网络与函数逼近等。在神经网络逼近复杂性和稀疏逼近等方面有较好的学术积累。已在IEEE TPAMI（5），IEEE TIT，IEEE TIP，IEEE TNNLS（2），ACHA（2），IP，PR, KBS, AAAI，IEEE SPL(3), SP（2），NN，ICASSP(4), 中国科学（5）, 计算机学报，数学学报，电子学报（3）等国内外顶级学术期刊发表90余篇学术论文。主持国家自然科学基金5项， 应邀作大会特邀报告30余次。