报告人：王建军（西南大学）

时间：2022年04月13日16:10开始

腾讯会议ID：608 619 593

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*n3 tensor 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 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. Conducting experiments on both synthetic data and real-world data, we show the effectiveness of the proposed methods.

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。 已在IEEE Transactions on Pattern Analysis and Machine Intelligence（2）, IEEE Transactions on Image Processing, 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。

个人网页：http://math.swu.edu.cn/s/math/index2jiaoshoutea14sub1.html

邀请人：李寒宇

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