Recovering structured signals: atoms, matrix separation, and applications

恢复结构化信号：原子、矩阵分离和应用

• 批准号: 2307827
• 负责人: Xuemei Chen
• 金额: $ 19.9万
• 依托单位: University of North Carolina at Wilmington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307827&HistoricalAwards=false
• 关键词: Recovering; structured; signals; atoms; matrix

High dimensional data sensing, representation, and recovery that utilize the data’s intrinsic low dimensionality have become pervasive in many applications, including signal processing, computer vision, and machine learning. This project involves the development and analysis of new solutions for sensing and analyzing high dimensional data, inspired by the electrodermal activity (EDA) signal decomposition problem. A cleaner EDA decomposition allows scientists and data analysts to extract better features to serve a variety of tasks such as market research, seizure detection, human stress analysis, and emotion recognition, leading to social and economical benefits. In particular, this project aims to increase the recovery rate of medication-assisted treatment in rehabilitation centers. Many of the expected results will also be applicable to other imaging modalities as well as machine learning applications. Undergraduate and master students from diverse backgrounds will be mentored as part of this project. The students will also have opportunities to work with peers and researchers to better understand and contribute to real world applications. This project aims to recover structured signals that are intrinsically low dimensional with significantly subsampled measurements. The project involves an analysis of the sensing conditions needed for the subsampled measurements and how they benefit the structured signals expressed in terms of few atoms. A framework for a generalized matrix decomposition will also be developed, which will be suitable for the EDA decomposition setting. Efficient algorithms for solving the associated novel optimization problems will also be developed and implemented. The new framework developed in this project combined with rigorous theoretical guarantees are expected to strengthen existing partnerships with other disciplines such as psychology and industry.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.

在许多应用中，包括信号处理，计算机视觉和机器学习在内，利用数据内在的低维度的高维数据灵敏度，表示和恢复已变得普遍存在。该项目涉及对敏感性的新解决方案的开发和分析，并受到受皮肤活动（EDA）信号分解问题的启发的高维数据。更清洁的EDA分解使科学家和数据分析师能够提取更好的功能，以服务各种任务，例如市场研究，癫痫发作检测，人力压力分析和情感认可，从而带来社会和经济利益。特别是，该项目旨在提高康复中心药物辅助治疗的恢复率。许多预期的结果也将适用于其他成像方式以及机器学习应用程序。来自潜水员背景的本科生和硕士学生将被视为该项目的一部分。学生还将有机会与同行和研究人员合作，以更好地理解并为现实世界的应用做出贡献。该项目旨在恢复尺寸本质上较低的结构化信号，并进行显着下采样的测量。该项目涉及对测得测量所需的传感条件的分析，以及它们如何使以几种原子表示的结构化信号受益。还将开发用于广义基质分解的框架，该框架适用于EDA分解设置。还将开发和实施用于解决相关新型优化问题的有效算法。该项目中开发的新框架与严格的理论保证有望加强与心理学和行业等其他学科的现有合作伙伴关系。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估标准来通过评估来获得支持的。