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稀疏恢复及其应用研讨会

2022年10月27日 15:13  点击:[]



稀疏恢复及其应用研讨会

2022 10 29

腾讯会议



会议简介

为了加强稀疏恢复及其应用方面的学术交流,必赢3003am数学

科学学院和浙江理工大学理学院将举办稀疏恢复及其应用研讨会

会议主题包括数据科学中的逼近论问题,例如稀疏恢复、相位恢

复、压缩感知等。研讨会的目的是分享最新研究进展、寻求难题解

决方案、探讨未来合作课题。

会议平台

腾讯会议

会议 ID540787259

会议时间

10 29 全天

主办单位

必赢3003am

浙江理工大学理学院数学科学系

会议发起人

李崇君,必赢3003am(chongjun@dlut.edu.cn

沈益,浙江理工大学理学院数学科学系(yshen@zstu.edu.cn

会议联系人

钟轶君,浙江理工大学理学院 (zhongyijun@zstu.edu.cn 电话:15998582681)


会议日程

10 29 日,周六

上午场 主持人:李崇君

08:25-08:30 开幕式,

学术报告

08:30-09:15 李松, Two Applications of IHT to Non-smooth Objective

Functions

09:15-10:00 谌稳固, Sparse Representation and Sparse Recovery of Sig

nals

10:00-10:10 间歇,

10:10-10:55 许志强, 稀疏信号的相位恢复

10:55-11:40 沈益, Open Questions on Sparse Representations in Union

bases

下午场 主持人:沈益

14:00-14:45 温金明, A ReLU-based Hard-thresholding Algorithm for

Non-negative Sparse Signal Recovery

14:45-15:30 杨建斌, 基于小波分析方法的保特征函数逼近及其应用

15:30-15:40 间歇,

15:40-16:25 但炜, Dictionary based sparse phase retrieval

16:25-17:10 黄猛, Phase Retrieval: Theory and Algorithms


报告摘要及报告人简介


Two Applications of IHT to Non-smooth Objective

Functions
李松
浙江大学
In this talk, we consider projected subgradient method under sparsity con
strains. Our first contribution is the convergence analysis of the binary iterative
hard thresholding (BIHT) algorithm which is a state-of-the-art recovery algo
rithm in one-bit compressive sensing. The basic idea of the convergence analysis
is to view BIHT as a kind of projected subgradient method under sparsity con
strains. If measurement matrices satisfy l 1 restricted isometry property, we obtain
a tighter error bound. Our second contribution is providing an adaptive iterative
hard thresholding (AIHT_1) method to solve LAD problems with sparsity con
straints. The sequence generated by AIHT_1 converges to ground truth linearly
under the l 1 restricted isometry property condition. The numerical experiments
show that our proposed projected subgradient methods are very simple to imple
ment, robust to sparse noise, and effective for sparse recovery problems.
李松,浙江大学求是特聘教授,博士生导师,研究方向包括;压缩感知理论、
低秩矩阵恢复理论、相位恢复理论以及双线性反问题(如 : 盲卷积重构问题)。曾
担任浙江省科协委员,中国数学会理事。曾多次担任国家自然科学基金委员会
数理学部重点、人才与面上项目会评专家。目前担任浙江省数学会副理事长,高
校应用数学学报编委。主要从事应用调和分析及相关领域的研究工作,其中包
: 压缩感知、低秩矩阵恢复、小波分析理论与应用、相位恢复、盲去卷积等。
到目前为止在国际数学、应用数学、数学与信息交叉以及数学与信号处理交叉
等领域著名期刊发表了 90 余篇学术论文(其中包括: J. Approx.Theory, Adv.
Comput. Math, Appl. Comput. Harmon. Anal, Inverse Problem, IEEE Trans.
Inform.Theory, IEEE Trans. Signal. Process 等) ; 主持了包括国家自然科学基
金重点项目、面上项目以及浙江省重大科技项目等 7 项基金项目,作为第一完
成人曾获得教育部自然科学二等奖( 2013 )。


Sparse Representation and Sparse Recovery of Signals

谌稳固
北京应用物理与计算数学研究所
The sparse representation theory and non-convex optimization play important
roles in compressed sensing and machine learning. In this talk, I will focus on
the sparse decomposition of signals and some applications in sparse recovery of
signals via non-convex minimization.
谌稳固,北京应用物理与计算数学研究所研究员,博士生导师,主要从事调
和分析、压缩感知、机器学习的理论及应用研究,在 Applied and Computational
Harmonic Analysis IEEE Transactions on Information Theory, Inverse Prob
lems,Inverse Problems and Imaging, SIAM Journal on Imaging Sciences, Signal
Processing 等学术刊物发表科研论文 60 余篇。


稀疏信号的相位恢复

许志强
中国科学院数学与系统科学研究院
压缩感知理论表明可利用信号的稀疏性,通过少量观测对信号进行恢复。压
缩感知中的观测是线性观测。但在很多应用中,人们可遇到非线性观测。本报
告主要介绍如何将压缩感知中的结果扩展到无相位观测。
许志强,中国科学院数学与系统科学研究院研究员,冯康首席研究员。研究
领域包括逼近论、计算调和分析、离散数学等,尤其对采样理论,压缩感知,以
及相位恢复等领域感兴趣。一方面,他将纯粹数学中的研究方法引入到计算调
和分析,系统发展了相位恢复的代数簇方法,从而对一些困难问题得到实质性
进展;另一方面,将逼近论中样条函数和代数理论相结,从而解决了多个猜想和
公开问题。 2020 年获得国家杰出青年基金资助。曾经担任中国数学会计算数学
分会秘书长( 2014.12-2019.8 ),现担任《 IEEE Trans. Information Theory , J.
Comp Math. , Numerical Mathematics: Theory, Methods and Applications
等三个国际期刊编委。


Open Questions on Sparse Representations in Union bases

沈益
浙江理工大学
We consider sparse representations of signals from redundant dictionaries which
are unions of several orthonormal bases. The spark introduced by Donoho and
Elad plays an important role in sparse representations. However, numerical com
putations of sparks are generally combinatorial. For unions of several orthonormal
bases, two lower bounds on the spark via the mutual coherence were established
in previous work. We constructively prove that both of them are tight. Our
main results give positive answers to Gribonval and Nielsen’s open problem on
sparse representations in unions of orthonormal bases. Constructive proofs rely
on a family of mutual unbiased bases which first appears in quantum information
theory. It is joint work with Prof. Song Li, Dr. Yuan Shen and Chenyun Yu.
沈益,浙江理工大学数学科学系教授,浙江省应用数学研究会副理事长,毕
业于浙江大学数学系获应用数学博士学位 ( 导师:李松教授 ) 。从事应用调和分
析,逼近论相关领域的研究。研究内容为信号处理,数据分析中的数学问题与方
法。主持国家自然科学基金面上项目,优秀青年科学基金项目,浙江省杰出青年
基金项目等省部级项目。在 Appl Comput Harmon A IEEE T Inform Thoery
IEEE T Signal Proces Comput Aided Geom D 等期刊发表论文 20 余篇。


A ReLU-based Hard-thresholding Algorithm for

Non-negative Sparse Signal Recovery
温金明
暨南大学
In numerous applications, such as DNA microarrays, face recognition and
spectral unmixing, we need to acquire a non-negative K-sparse signal x from
an underdetermined linear model y= Ax+v. To recover such sparse signals, we
propose a ReLU-based hard-thresholding algorithm (RHT) and then develop two
sufffficient conditions of stable recovery with RHT, which are respectively based
on the restricted isometry property (RIP) and mutual coherence of the sens
ing matrix A. As far as we know, these two sufffficient conditions are the best
for hard-thresholding-type algorithms. Finally, we perform extensive numeri
cal experiments to show that RHT has better overall recovery performance and
more efffficient than the non-negative least squares (NNLS) algorithm, some hard
thresholding-type algorithms including the iterative hard-thresholding (IHT) al
gorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard
thresholding algorithm (NSIHT) and Newton-step-based hard-thresholding pur
suit (NSHTP), and Non-Negative orthogonal matching pursuit (NNOMP), Fast
NNOMP (FNNOMP) and Support-Shrinkage NNOMP (SNNOMP), which are
variants of orthogonal matching pursuit (OMP) for recovering non-negative sparse
signals.
温金明,暨南大学教授、博导、国家高层次青年人才、广东省青年珠江学者,主
持国家自然科学基金面上项目 2 项,省级项目 4 项; 2015 6 月博士毕业于加拿
大麦吉尔大学数学与统计学院。从 2015 3 月到 2018 9 月,温教授先后在法
国科学院里昂并行计算实验室、加拿大阿尔伯塔大学、多伦多大学从事博士后研
究工作。温教授的研究方向是整数信号和稀疏信号恢复的算法设计与理论分析,
以第一作者 / 通讯作者在 Applied and Computational Harmonic Analysis IEEE
Transactions on Information Theory IEEE Transactions on Signal Processing
等期刊和会议发表 50 余篇学术论文。


基于小波分析方法的保特征函数逼近及其应用

杨建斌
河海大学
在科学计算和工程等领域中,常需要根据测量数据对函数进行逼近。一方面,
测量机制可描述为相关物理系统的反问题模型,数值求解面临着非线性和不适
定性等特点;另一方面,目标函数可能非光滑,含有间断、跳跃等重要的几何特
性。这些特点决定了非光滑函数逼近是一个有着广泛应用背景但同时具有挑战
性的课题。报告主要讨论保特征的函数逼近理论和相关应用,包括基于小波多
尺度分析和稀疏表示方法,研究函数的逼近性质和保特征的能力,以及非光滑
函数逼近方法在图像恢复、分子动力学等领域的一些应用。
杨建斌,河海大学教授,博士生导师。 2010 年在浙江大学获得应用数学博士
学位,导师李松教授。 2013 年、 2017 年在新加坡国立大学从事访问学者工作。
目前研究兴趣主要在小波分析及应用、函数逼近论、数据科学等领域。主持国
家基金面上项目、青年项目等,在 SIAM J. Numer. Anal. Appl. Comput.
Harmon. Anal. 等期刊发表学术论文 20 余篇。


Dictionary based sparse phase retrieval

但炜
深圳技术大学
In this talk, we explore the l 1 synthesis and optimal dual based l 1 analysis
models for the phase retrieval problem to signals that are not sparse in an or
thonormal basis but rather in an overcomplete dictionary. We show the proposed
two models are equivalent. The uniqueness and stability of these methods are
investigated. An alternating iterative algorithm is also proposed.
但炜,深圳技术大学副教授,硕士生导师,深圳市高层次人才,主持国家自
然科学基金,广东省自然科学基金项目,曾荣获深圳技术大学优秀教师称号,以
第一作者或通讯作者发表科研学术论文十余篇。


Phase Retrieval: Theory and Algorithms

黄猛
北京航空航天大学
In this talk, we give a brief survey to the recent development of theory and al
gorithms for phase retrieval problem. First, we give a remarkable result that there
is no linear convergence algorithm for solving the Fourier phase retrieval problem.
This demystifies the phenomenon why no provable algorithm has been proposed
over the past few decades. Secondly, we consider the generalized phase retrieval
and show that the randomized Kaczmarz method for solving the complex-valued
phaseless equations is linear convergent. This gives a positive answer to the
conjecture proposed by Tan and Vershynin. Finally, we show that the modified
amplitude-based model for generalized phase retrieval possesses the benign geo
metric landscape, which provides a theoretical guarantee for the convergence of
gradient descent algorithms, even with random initialization.
Meng Huang received the Ph.D. degree from Academy of Mathematics and
Systems Science, Chinese Academy of Sciences, China, under the supervision of
Prof. Zhiqiang Xu, in 2019. In 2021, he was a Postdoctoral Scholar at Hong Kong
University of Sciences and Technology. Since January 2022, he has been with the
Beihang University, where he is currently an associate professor of mathematics.
His research interests include phase retrieval, matrix sensing, and mathematical
data science.


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