CIF:Medium:Convex Optimization for Blind Inverse Problems

CIF：中：盲逆问题的凸优化

基本信息

批准号：
2203060
负责人：
Youjian Liu
金额：
$ 75.3万
依托单位：
University of Colorado at Boulder
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-12-01 至 2024-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2203060&HistoricalAwards=false
关键词：
CIF Medium Convex Optimization Blind

项目摘要

One of the fundamental tasks in processing sensor and imaging datais to solve an inverse problem, determining the nature of somefundamental structure that produced that data. Such problems areoften underdetermined, meaning that the number of unknowns exceedsthe number of observations, and these problems are even morecomplicated in the blind setting, where the fundamental structuremay undergo some unknown transformation en route to the sensor.This project considers a number of such blind inverse problems,including non-stationary deconvolution, where an unknown pointspread function changes over time; multi-band signalidentification, where line spectrum estimation is extended tosignals with multiple narrow frequency bands; super-resolutionradar imaging, where extended and accelerating targets may causeunwanted spreading in the delay-Doppler space; and simultaneousblind deconvolution and phase retrieval. Conventionally, all ofthese problems have been studied separately. This projectinvestigates all of the problems jointly under a unifyingoptimization and analysis framework.By modeling unknown transformation operators using subspaces, theinvestigators transform each non-convex inverse problem into alinear inverse problem of recovering a structured signal. Thissignal is a parsimonious mixture of lifted atoms generated by theoriginal atomic set, allowing the investigators to enforce itssimplicity using a new atomic norm. The investigators develop novelanalysis techniques to demonstrate the optimality of this frameworkby deriving sampling complexities that achieve theinformation-theoretical limits, calculating mean-squared denoisingerrors that match the minimax rates, and developing parameterestimation bounds that approach the Cramer-Rao bounds. The projectbuilds on the investigators' combined expertise in signalprocessing, convex optimization in continuously parameterizedinverse problems, and geometric modeling.

处理传感器和成像数据以解决反问题的基本任务之一，确定了产生该数据的某些基础结构的性质。此类问题通常不确定，这意味着未知数的数量超过了观察的数量，这些问题甚至在盲目的环境中变得毫无份额，在这种情况下，基本的结构性在传感器的途径中经历了一些未知的转变。该项目考虑了许多此类盲人问题，包括多个违反问题，包括非机构的衰弱，既定时间都会变化，而超过了时间差异。多带信号识别，其中线频谱估计是具有多个窄频带的扩展信号；超级分辨率成像，扩展和加速目标可能导致在延迟多普勒空间中扩散；以及同时蓝色的反卷积和相位检索。从传统上讲，所有这些问题均已分别研究。该项目对所有问题进行了对统一和分析框架的共同问题。通过使用子空间对未知的转换操作员进行建模，调查器将每个非convex逆问题转换为恢复结构化信号的逆问题。这种信号是理论原子集产生的举起原子的简约混合物，使研究人员能够使用新的原子范围来实施其效率。研究人员开发了新型分析技术，以证明该框架的最佳性，通过得出采样复杂性，以实现知识理论的限制，计算均方根的DeNoisingerrors，与最小值速率相匹配，并开发出接近Cramer-Rao界限的参数估算结合。研究人员在信号处理，连续参数化问题中的凸优化和几何建模方面的综合专业知识和几何建模。

项目成果

期刊论文数量（10）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Data-driven Support Recovery for Sparse Signals with Non-stationary Modulation

非平稳调制稀疏信号的数据驱动支持恢复

DOI：
10.1109/icmla52953.2021.00262
发表时间：
2021
期刊：
2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA
影响因子：
0
作者：
Xie, Youye;Wakin, Michael B.;Tang, Gongguo
通讯作者：
Tang, Gongguo

Contaminated Multiband Signal Identification Via Deep Learning