Taming Nonlinear Inverse Problems: Theory and Algorithms

驯服非线性反问题：理论与算法

• 批准号: 2126634
• 负责人: Yuejie Chi
• 金额: $ 38万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2126634&HistoricalAwards=false
• 关键词: Taming; Nonlinear; Inverse; Problems; Theory; Taming; Nonlinear; Inverse; Problems; Theory

While modern developments in large-scale sensing and imaging modalities bring great premise in discovering novel scientific phenomena and improving the quality-of-life, making sense of the sensed data in an efficient and accurate manner require transformative designs of scalable and effective optimization methods for solving inverse problems that go beyond classical linear models. There is a significant need to advance the theory, algorithms, and applications of nonlinear inverse problems, where the collected data exhibit a nonlinear relationship with respect to the unknowns being sought after. Focused on taming nonlinear inverse problems, this project will be tightly integrated with education, outreach and dissemination activities including mentoring both graduate and undergraduate students with diverse backgrounds, developing courses and monographs on nonlinear inverse problems in data science, and organizing special sessions at suitable conference venues.The intellectual goal of this project is to develop theoretical and algorithmic foundations for solving nonlinear inverse problems, including the design and analysis of efficient algorithms with provable guarantees, characterization of fundamental trade-offs between resources (sample, computational and memory complexities, signal-to-noise ratio, etc.) and performance (statistical error rates, resolution, etc.), and validations on real data whenever applicable. The project seeks to leverage the diversity of multiple measurements and the invariance of data representation in the algorithm designs to minimize complexity and improve performance. The tools and techniques developed in this project will lead to further cross fertilization among the fields of signal processing, inverse problems, optimization theory, and machine learning.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.

尽管大规模传感和成像方式的现代发展在发现新颖的科学现象和改善生活质量方面带来了巨大的前提，以有效而准确的方式了解感知的数据需要可扩展有效的优化方法，以求解超出经典的线性模型的逆问题的可扩展和有效优化方法。非线性逆问题的理论，算法和应用非常需要，在该理论，算法和应用中，收集到的数据与所寻求的未知数表现出非线性关系。该项目专注于论到非线性逆问题，将与教育，外展和传播活动紧密融合，包括指导具有不同背景的研究生和本科生，开发课程和专着数据科学中的非线性反问题，并在适当的会议场所组织特殊范围的特殊性目标，包括在适当的会议上进行特殊目标。具有可证明保证的有效算法，对资源（样本，计算和记忆复杂性，信噪比的比率等）之间的基本权衡表征和绩效（统计错误率，解决方案等）以及对实际数据的验证。该项目旨在利用多个测量值的多样性以及算法设计中数据表示的不变性，以最大程度地降低复杂性并提高性能。该项目中开发的工具和技术将导致信号处理，反问题，优化理论和机器学习领域之间进一步交叉施肥。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审查标准通过评估来获得支持的。