报告题目:Matrix Computations in Signal Recovery

 

报告人:高卫国教授(复旦大学)

 

报告时间:2022年12月26日(周一)9:00-11:00

 

腾讯会议:898 938 573

 

报告摘要:We present some matrix computations in signal processing in this talk. First, we study matrix completion based on the low rank Hankel structure in the Fourier domain. It is shown that matrices with this structure can be exactly recovered by solving a convex optimization program provided the sampling complexity is nearly optimal. Then, we consider the problem of resolving point sources from given samples at the low end of the spectrum when the point spread functions lie in low dimensional subspace, which can be reformulated as a matrix recovery problem. By exploiting the low rank structure of the vectorized Hankel matrix associated with the target matrix, a convex approach called Vectorized Hankel Lift is proposed for the matrix recovery. Finally, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements collected by a uniform array of sensors. We prove novel non-asymptotic stability bounds for MUSIC and ESPRIT as a function of the noise standard deviation, number of snapshots, source amplitudes, and support. This is joint work with Jinchi Chen, Weilin Li, Wenjing Liao, Sihan Mao, Ke Wei and Zengying Zhu.

 

报告人简介:高卫国,复旦大学韦德bv1946游戏教授、博士生导师,大数据学院副院长,研究方向为高性能矩阵计算及其在物质科学和数据科学中的应用,包括线性和非线性特征值问题、大规模科学与并行计算、电子结构计算与鞍点计算、数据科学中的数值算法等。研究成果先后在计算数学、计算机、物理、化学、工程和控制等学科杂志和计算机会议发表论文约50篇,主持和参与多个高性能软件包开发。高卫国教授是自然科学基金委重大项目、科技部973、教育部数理基础项目子课题负责人,主持自然科学基金委面上项目、上海市科委基础研究项目等,参与自然科学基金委重大项目、科技部“变革型技术关键科学问题”等课题,并且和山东电力科学研究院、华为技术有限公司、上海期货交易所等建立了横向合作课题。高卫国教授担任国内外多个期刊杂志的编委。

 

邀请人:黄金枝