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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.

相位恢复（PR）或“从无相测量中恢复信号”是在许多信号/图像采集领域中出现的问题，例如傅立叶重叠关联成像和子衍射成像，其中只能测量信号或图像的某些线性投影的幅度（强度）。虽然PR是一个经典的问题，但近年来，人们对PR重新产生了兴趣，其目标是开发可证明正确和快速的算法。然而，大多数这项工作并没有假设信号的任何结构，因此必然需要比未知信号长度更多的测量。当移动到非常高的分辨率成像时，这可能是一个挑战，因为它意味着数据采集的成本成比例地更高（在时间、传感器数量或功耗方面）。时变场景的动态成像，例如，活的生物样本，带来了更大的挑战。我们利用两种常见的结构假设-稀疏性和低秩-来解决这个限制，以实现快速，低成本的高分辨率成像。一组不同的研究生和本科生参与了这项研究。该项目开发了第一套可证明正确的，快速的，低样本复杂度的算法，用于在两种设置下的无相位低秩矩阵恢复。第一个涉及从矩阵的每一列的无相位线性投影中恢复。当（矢量化的）图像序列被低秩矩阵很好地近似时，这在无相动态成像中找到应用，例如，缓慢变化的动态场景。第二种设置涉及从整个矩阵的无相位线性投影中恢复。当图像本身可以被建模为低秩时，这是有用的。该项目还开发了可证明的快速和统计上有效的稀疏PR算法，并探索了学习广义线性模型的扩展。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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）

Phaseless Subspace Tracking

无相子空间跟踪

DOI：
发表时间：
2018
期刊：
IEEE Global Conference on Signal and Information Processing
影响因子：
0
作者：
Nayer, S;Vaswani, N
通讯作者：
Vaswani, N

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

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

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

PhaST: Model-free Phaseless Subspace Tracking

PhaST：无模型无相子空间跟踪

DOI：
10.1109/icassp.2019.8683458
发表时间：
2019
期刊：
ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
影响因子：
0
作者：
Seyedehsara Nayer;Namrata Vaswani
通讯作者：
Namrata Vaswani