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

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.

虽然大规模传感和成像模式的现代发展为发现新的科学现象和提高生活质量带来了很大的前提，但以有效和准确的方式理解传感数据需要对可扩展和有效的优化方法进行变革性设计，以解决超越经典线性模型的逆问题。有一个重要的需要，以推进理论，算法和应用的非线性反问题，其中收集的数据显示出一个非线性的关系，相对于所寻求的未知。该项目以驯服非线性逆问题为重点，将与教育、推广和传播活动紧密结合，包括指导不同背景的研究生和本科生，开发数据科学中非线性逆问题的课程和专著，以及在适当的会议场所组织特别会议。该项目的智力目标是为解决非线性逆问题开发理论和算法基础，包括设计和分析具有可证明保证的高效算法，表征资源（样本，计算和内存复杂性，信噪比等）和性能（统计错误率，分辨率等）之间的基本权衡，以及在适用的情况下对实际数据进行验证。该项目旨在利用算法设计中多种测量的多样性和数据表示的不变性，以最大限度地降低复杂性并提高性能。本项目开发的工具和技术将进一步促进信号处理、逆问题、优化理论和机器学习等领域的交叉发展。该奖项反映了美国国家科学基金会的法定使命，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。

项目成果

Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements

• 发表时间: 2021-04
• 期刊: J. Mach. Learn. Res.
• 作者: Tian Tong;Cong Ma;Ashley Prater-Bennette;Erin E. Tripp;Yuejie Chi

Deep Unfolded Tensor Robust PCA With Self-Supervised Learning

• DOI: 10.1109/icassp49357.2023.10095485
• 发表时间: 2022-12
• 期刊: ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 作者: Harry Dong;Megna Shah;S. Donegan;Yuejie Chi

Local Geometry of Nonconvex Spike Deconvolution From Low-Pass Measurements

• DOI: 10.1109/jsait.2023.3262689
• 发表时间: 2022-08
• 期刊: IEEE Journal on Selected Areas in Information Theory
• 作者: Maxime Ferreira Da Costa;Yuejie Chi

Accelerating ILL-Conditioned Robust Low-Rank Tensor Regression

• DOI: 10.1109/icassp43922.2022.9746705
• 发表时间: 2022-05
• 期刊: ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 作者: Tian Tong;Cong Ma;Yuejie Chi

The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing

• DOI: 10.48550/arxiv.2302.01186
• 发表时间: 2023-02
• 作者: Xingyu Xu;Yandi Shen;Yuejie Chi;Cong Ma