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“从无相测量中恢复信号”是许多信号/图像采集领域中出现的一个问题，例如傅里叶叠层成像和亚衍射成像，其中仅确定某些线性投影的幅度（强度）可以测量信号或图像的。虽然 PR 是一个经典问题，但近年来人们对 PR 重新产生了兴趣，目标是开发可证明正确且快速的算法。然而，这项工作的大部分内容并没有假设信号的任何结构，因此必然需要比未知信号的长度更多的测量。当转向超高分辨率成像时，这可能是一个挑战，因为这意味着数据采集成本（在时间、传感器数量或功耗方面）成比例地更高。时变场景（例如活体生物样本）的动态成像提出了更大的挑战。我们通过利用两类常见的结构假设（稀疏性和低秩）来解决这一限制，以实现快速且低成本的高分辨率成像。各种各样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、快速且低样本复杂度的算法，用于在两种设置下进行无相低秩矩阵恢复。第一个涉及从矩阵每列的无相线性投影中恢复。当（矢量化）图像序列通过低秩矩阵很好地近似时，例如缓慢变化的动态场景，这在无相动态成像中得到应用。第二种设置涉及从整个矩阵的无相线性投影恢复。当图像本身可以被建模为低等级时，这非常有用。该项目还开发了可证明快速且统计上有效的稀疏 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。