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:
  • 金额:
    $ 75.3万
  • 依托单位:
  • 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

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的基本任务之一是解决一个反问题,确定产生该数据的某些基本结构的性质。这样的问题通常是不确定的,这意味着未知的数量超过了观测的数量,这些问题在盲设置中甚至更加复杂,在盲设置中,基本结构可能在通往传感器的途中经历一些未知的转换。该项目考虑了许多这样的盲逆问题,包括非平稳反卷积,其中未知的点扩散函数随时间变化;多波段信号识别,其中线谱估计扩展到具有多个窄频带的信号;超分辨率雷达成像,其中扩展和加速目标可能在延迟多普勒空间中造成不必要的扩散;同时进行盲反卷积和相位恢复。通常,所有这些问题都是分开研究的。本项目在统一的优化分析框架下,对所有问题进行联合研究。通过利用子空间对未知变换算子进行建模,研究人员将每个非凸逆问题转化为恢复结构化信号的线性逆问题。该信号是由原始原子集产生的提升原子的简约混合物,允许研究人员使用新的原子规范来强制其简单性。研究人员开发了新的分析技术,通过推导达到信息理论极限的采样复杂性,计算与极大极小率匹配的均方去噪误差,以及开发接近Cramer-Rao界限的参数估计界限,来证明该框架的最优性。该项目建立在研究人员在信号处理、连续参数化逆问题中的凸优化和几何建模方面的综合专业知识的基础上。

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
Contaminated Multiband Signal Identification Via Deep Learning
Compressive Sensing With Wigner $D$-Functions on Subsets of the Sphere
维格纳 $D$ 球体子集上的压缩感知函数
  • DOI:
    10.1109/tsp.2022.3223848
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    5.4
  • 作者:
    Valdez, Marc Andrew;Yuffa, Alex J.;Wakin, Michael B.
  • 通讯作者:
    Wakin, Michael B.
Green’s function estimation by seismic interferometry from limited frequency samples
通过有限频率样本的地震干涉测量格林函数估计
  • DOI:
    10.1016/j.sigpro.2022.108863
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    4.4
  • 作者:
    Jayne, Justin;Wakin, Michael B.;Snieder, Roel
  • 通讯作者:
    Snieder, Roel
Gridless DOA Estimation Under the Multi-Frequency Model
多频模型下无网格DOA估计
  • DOI:
    10.1109/icassp43922.2022.9746951
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Wu, Yifan;Wakin, Michael B.;Gerstoft, Peter
  • 通讯作者:
    Gerstoft, Peter
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Youjian Liu其他文献

Duality and Optimization for Generalized Multi-Hop MIMO Amplify-and-Forward Relay Networks With Linear Constraints
具有线性约束的广义多跳 MIMO 放大转发中继网络的对偶性和优化
An Efficient Algorithm and Hardware Architecture for Maximum-Likelihood Based Carrier Frequency Offset Estimation in MIMO Systems
MIMO 系统中基于最大似然的载波频偏估计的高效算法和硬件架构
  • DOI:
    10.1109/access.2018.2869114
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    3.9
  • 作者:
    Mingda Zhou;Zhe Feng;Youjian Liu;Xinming Huang
  • 通讯作者:
    Xinming Huang

Youjian Liu的其他文献

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{{ truncateString('Youjian Liu', 18)}}的其他基金

Collaborative Research: SWIFT: Enabling Intelligent Pinpoint Space-Spectrum Utilization and Sharing
合作研究:SWIFT:实现智能精确空间频谱利用和共享
  • 批准号:
    2128659
  • 财政年份:
    2022
  • 资助金额:
    $ 75.3万
  • 项目类别:
    Standard Grant
Collaborative Research: Practical Signal Design for Interference Management in Wireless Communication Networks
合作研究:无线通信网络干扰管理的实用信号设计
  • 批准号:
    1408604
  • 财政年份:
    2014
  • 资助金额:
    $ 75.3万
  • 项目类别:
    Standard Grant
PFI:AIR - TT: Technology for Sustainable Growth of Wireless Communication Capacity
PFI:AIR - TT:无线通信容量可持续增长的技术
  • 批准号:
    1414250
  • 财政年份:
    2014
  • 资助金额:
    $ 75.3万
  • 项目类别:
    Standard Grant
Collaborative Research: A Universal Cooperative Communication System-on-Chip
协作研究:通用协作通信片上系统
  • 批准号:
    0725915
  • 财政年份:
    2007
  • 资助金额:
    $ 75.3万
  • 项目类别:
    Standard Grant

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