Recovering structured signals: atoms, matrix separation, and applications

利用数据固有的低维度的高维数据感测、表示和恢复已经在许多应用中变得普遍，包括信号处理、计算机视觉和机器学习。该项目涉及开发和分析用于感测和分析高维数据的新解决方案，其灵感来自皮肤电活动（EDA）信号分解问题。更清晰的EDA分解使科学家和数据分析师能够提取更好的特征，以服务于各种任务，如市场研究，癫痫发作检测，人类压力分析和情感识别，从而带来社会和经济效益。特别是，该项目旨在提高康复中心药物辅助治疗的康复率。许多预期的结果也将适用于其他成像模式以及机器学习应用。来自不同背景的本科生和硕士生将作为该项目的一部分进行指导。学生也将有机会与同行和研究人员合作，以更好地了解和促进真实的世界的应用。该项目旨在恢复结构化信号，本质上是低维的显着二次采样测量。该项目涉及分析二次采样测量所需的传感条件，以及它们如何使以少数原子表示的结构化信号受益。一个广义矩阵分解的框架也将开发，这将是适合的EDA分解设置。解决相关的新的优化问题的有效算法也将开发和实施。该项目中开发的新框架与严格的理论保证相结合，有望加强与心理学和工业等其他学科的现有合作伙伴关系。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.