CIF: Small: Signal Recovery Beyond Minimization: A Monotone Inclusion Framework

CIF：小：超越最小化的信号恢复：单调包含框架

• 批准号: 2211123
• 负责人: Patrick Combettes
• 金额: $ 40.96万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2211123&HistoricalAwards=false
• 关键词: CIF; Small; Signal; Recovery; Beyond

The problem of extracting information from data is at the core of many tasks in signal processing and machine learning. The importance of this problem stems from its pervasiveness in numerous areas of science and engineering, including medical imaging, geophysics, astronomy, forecasting, nondestructive testing, seismology, telecommunications, social media analysis, speech analysis, healthcare, and homeland security. This project investigates foundational principles governing the mathematical formulation of signal recovery and machine learning problems and develops new strategies and methodologies for data processing that significantly improve the efficiency of existing techniques and broadens their scope. The most prevalent methodology that has been used to formulate information-extraction tasks has been to associate a loss function with each piece of prior knowledge and each observation, and to minimize an aggregate of these functions. In recent years, an increasing number of problem formulations have emerged, which cannot be naturally reduced to tractable minimization problems and which are best captured by more general notions of equilibria. The broad goal of this project is to lay out the theoretical and computational foundations of a framework based on monotone-operator theory to model and aggregate prior knowledge and observations in data processing problems. The proposed framework encompasses the standard minimization setting as well as various forms of equilibria. It exploits the broad modeling capabilities of monotone operators, their rich theory, and the powerful machinery of monotone operator splitting algorithms to provide robust and efficient numerical solution methods. The impact of the theoretical findings and of the new methodologies resulting from this research is illustrated through applications to concrete signal recovery and machine-learning problems.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.

从数据中提取信息的问题是信号处理和机器学习中许多任务的核心。该问题的重要性源于其在许多科学和工程领域的普遍性，包括医学成像，地球物理学，天文学，预测，无损害测试，地震学，电信学，社交媒体分析，语音分析，医疗保健，医疗保健和国土安全。该项目调查了管理信号恢复和机器学习问题的数学表述的基本原理，并为数据处理开发了新的策略和方法，从而显着提高了现有技术的效率并扩大了其范围。最普遍的方法是用于制定信息划分任务的最普遍的方法是将损失函数与每个先验知识和每个观察结果相关联，并最大程度地减少这些功能的汇总。近年来，出现了越来越多的问题制剂，这些问题不能自然地减少到可拖动的最小化问题，并且最好被更一般的平衡概念捕获。该项目的广泛目标是阐明基于单调操作机构理论的框架的理论和计算基础，以建模和汇总数据处理问题中的先验知识和观察结果。所提出的框架涵盖了标准最小化设置以及各种形式的平衡。它利用了单调操作员的广泛建模功能，其丰富的理论以及单调操作员分裂算法的强大机械，以提供强大而有效的数值解决方案方法。通过应用于具体信号恢复和机器学习问题的应用，理论发现和这项研究产生的新方法的影响。该奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子优点和更广泛的影响审查标准通过评估来进行评估。

项目成果

A Variational Inequality Model for Learning Neural Networks

• DOI: 10.1109/icassp49357.2023.10095688
• 发表时间: 2022-10
• 期刊: ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 作者: P. Combettes;J. Pesquet;A. Repetti