CIF: Small: Structured High-dimensional Data Recovery from Phaseless Measurements

CIF：小型：从无相测量中恢复结构化高维数据

基本信息

批准号：
1815101
负责人：
Namrata Vaswani
金额：
$ 49.9万
依托单位：
Iowa State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-10-01 至 2022-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1815101&HistoricalAwards=false
关键词：
CIF Small Structured dimensional Data

项目摘要

Phase retrieval (PR), or 'signal recovery from phaseless measurements', is a problem that occurs in numerous signal/image acquisition domains, such as Fourier ptychography and sub-diffraction imaging, in which only the magnitude (intensity) of certain linear projections of the signal or image can be measured. While PR is a classical problem, in recent years there has been renewed interest in PR with the goal of developing provably correct and fast algorithms. Much of this work, however, does not assume any structure on the signal, and as a result necessarily requires more measurements than the unknown signal's length. This can be a challenge when moving to very high resolution imaging because it implies a proportionally higher cost of data acquisition (in terms of time, number of sensors, or power consumption). Dynamic imaging of time-varying scenes, e.g., live biological samples, poses an even greater challenge. We address this limitation by exploiting two common classes of structural assumptions - sparsity and low-rank -- to enable fast and low cost high-resolution imaging. A diverse group of graduate and undergraduate students is involved in the research.This project develops the first set of provably correct, fast, and low-sample-complexity algorithms for phaseless low rank matrix recovery in two settings. The first involves recovery from phaseless linear projections of each column of the matrix. This finds applications in phaseless dynamic imaging when the (vectorized) image sequence is well approximated by a low rank matrix, e.g., slow changing dynamic scenes. The second setting involves recovery from phaseless linear projections of the entire matrix. This is useful when the image itself can be modeled as being low rank. This project also develops provably fast and statistically efficient sparse PR algorithms and explores extensions to learning generalized linear models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

相位检索（PR）或“从无音测量值中恢复信号”是一个问题，它发生在许多信号/图像采集域中，例如傅立叶Ptychography和Sub-Diffraction Imaging，只能测量信号或图像的某些线性投影的大小（强度）。尽管PR是一个经典的问题，但近年来，人们对PR的兴趣重新引起了人们的兴趣，其目的是开发可证明的正确和快速算法。但是，这项工作的大部分都不假设信号上的任何结构，因此必定需要比未知信号的长度更高的测量值。在转移到非常高的分辨率成像时，这可能是一个挑战，因为它意味着数据获取的成本比例更高（在时间，传感器数量或功耗方面）。时间变化场景的动态成像，例如，实时生物样品，提出了更大的挑战。我们通过利用两个常见的结构假设（稀疏性和低阶）来解决这一限制，以实现快速和低成本的高分辨率成像。一组多样化的研究生和本科生参与了研究。该项目开发了第一个可证明的正确，快速和低样本的复杂算法，用于在两种情况下无音低级矩阵恢复。第一个涉及从矩阵的每一列的无相线线性投影中恢复。当（矢量化的）图像序列通过低等级矩阵（例如，缓慢变化的动态场景）很好地近似时，这发现了无相位动态成像中的应用。第二个设置涉及从整个矩阵的无相位线性投影恢复。当图像本身可以建模为低等级时，这很有用。该项目还开发了可证明的快速且统计上有效的稀疏PR算法，并探讨了学习通用线性模型的延伸。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛影响的评估标准来评估值得支持的。

项目成果

期刊论文数量（24）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Fast and Sample-Efficient Federated Low Rank Matrix Recovery From Column-Wise Linear and Quadratic Projections

DOI：
10.1109/tit.2022.3212374
发表时间：
2021-02
期刊：
IEEE Transactions on Information Theory
影响因子：
2.5
作者：
Seyedehsara Nayer;Namrata Vaswani
通讯作者：
Seyedehsara Nayer;Namrata Vaswani

Implicit Sparse Regularization: The Impact of Depth and Early Stopping

DOI：
发表时间：
2021-08
期刊：
ArXiv
影响因子：
0
作者：
Jiangyuan Li;Thanh V. Nguyen;C. Hegde;R. K. Wong
通讯作者：
Jiangyuan Li;Thanh V. Nguyen;C. Hegde;R. K. Wong

Provable Compressed Sensing With Generative Priors via Langevin Dynamics

通过 Langevin Dynamics 使用生成先验可证明压缩感知

DOI：
10.1109/tit.2022.3179643
发表时间：
2022
期刊：
IEEE Transactions on Information Theory
影响因子：
2.5
作者：
Nguyen, Thanh V.;Jagatap, Gauri;Hegde, Chinmay
通讯作者：
Hegde, Chinmay

ALTERNATING PHASE PROJECTED GRADIENT DESCENT WITH GENERATIVE PRIORS FOR SOLVING COMPRESSIVE PHASE RETRIEVAL

DOI：
10.1109/icassp.2019.8682811
发表时间：
2019-01-01
期刊：
2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
影响因子：
0
作者：
Hyder, Rakib;Shah, Viraj;Asif, M. Salman
通讯作者：
Asif, M. Salman

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