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重要前提，但以高效和准确的方式理解传感数据需要可扩展和有效的优化方法的变革性设计解决超越经典线性模型的逆问题。迫切需要推进非线性反问题的理论、算法和应用，其中收集的数据相对于所寻求的未知数表现出非线性关系。该项目以解决非线性反演问题为重点，将与教育、推广和传播活动紧密结合，包括指导具有不同背景的研究生和本科生，开发数据科学中非线性反演问题的课程和专着，并在适当的会议上组织特别会议该项目的智力目标是为解决非线性反问题奠定理论和算法基础，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）之间的基本权衡复杂性、信噪比等）和性能（统计错误率、分辨率等），并在适用时对实际数据进行验证。该项目寻求在算法设计中利用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。该项目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的进一步交叉融合。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力评估进行评估，认为值得支持。优点和更广泛的影响审查标准。

项目成果

Local Geometry of Nonconvex Spike Deconvolution From Low-Pass Measurements

低通测量中非凸尖峰反卷积的局部几何

• DOI: 10.1109/jsait.2023.3262689
• 发表时间: 2023-01
• 期刊: IEEE Journal on Selected Areas in Information Theory
• 作者: Ferreira Da Costa, Maxime;Chi, Yuejie
• 通讯作者: Chi, Yuejie

The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing

预处理在超参数化低阶矩阵传感中的威力

• 发表时间: 2023-07
• 期刊: Proceedings of the 40 th International Conference on Machine Learning
• 作者: Xu, Xingyu;Shen, Yandi;Chi, Yuejie;Ma, Cong
• 通讯作者: Ma, Cong

Deep Unfolded Tensor Robust PCA With Self-Supervised Learning

具有自监督学习功能的深度展开张量鲁棒 PCA

• DOI: 10.1109/icassp49357.2023.10095485
• 发表时间: 2023-06
• 期刊: Speech and Signal Processing (ICASSP
• 作者: Dong, Harry;Shah, Megna;Donegan, Sean;Chi, Yuejie
• 通讯作者: Chi, Yuejie

Accelerating Ill-Conditioned Robust Low-Rank Tensor Regression

加速病态鲁棒低阶张量回归

• DOI: 10.1109/icassp43922.2022.9746705
• 发表时间: 2022-05
• 期刊: Speech and Signal Processing (ICASSP
• 作者: Tong, Tian;Ma, Cong;Chi, Yuejie
• 通讯作者: Chi, Yuejie

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

缩放比例和可扩展性：来自不完整测量的可证明的非凸低阶张量估计

• 发表时间: 2022-01
• 期刊: Journal of machine learning research
• 影响因子: 6
• 作者: Tong, Tian;Ma, Cong;Prater;Tripp, Erin;Chi, Yuejie
• 通讯作者: Chi, Yuejie