Data-Driven Time-Frequency Analysis via Nonlinear Optimization

通过非线性优化进行数据驱动的时频分析

• 批准号: 1318377
• 负责人: Thomas Hou
• 金额: $ 30万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-12-01 至 2017-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1318377&HistoricalAwards=false
• 关键词: Data; Driven; Time; Frequency; Analysis

This investigator proposes to develop a new data-driven time-frequency analysis method to study nonlinear and non-stationary data. The key idea is to look for the sparsest time-frequency representation of a signal over the largest possible dictionary using nonlinear optimization. Such a method is motivated by physical applications and the need to extract instantaneous frequency and trend from multiscale data arising from many scientific and engineering applications. Although several methods have been introduced to extract instantaneous frequency from a multiscale signal, these methods suffer from various limitations and do not have a solid mathematical foundation. The data-driven time-frequency analysis method developed by this investigator and his colleagues provides a mathematically rigorous definition of instantaneous frequency. This investigator and his colleagues have developed an efficient nonlinear matching pursuit method based on L1-regularized nonlinear least squares to decompose the signal. This method can be used to extract physically meaningful information of the signal such as instantaneous frequency and trend. The preliminary results show that this method can decompose a wide range of physical signals accurately and efficiently. Applications of this method to some real world data from geo-science and biomedical applications have led to some new discoveries. One of the main objectives of this proposal is to carry out a rigorous convergence study of this method and apply it to solve some challenging real world problems in biomedical and geo-science applications. Developing effective data analysis methods is an important path to understand some hidden patterns such as trend and cycles from the massive amount of data. So far, most data analysis methods use a predetermined basis to process data. Most of these methods can handle only linear and stationary data. To better understand the physical mechanisms hidden in data, one needs to develop effective methods that can handle the non-stationarity and nonlinearity of the data. Such methods require the use of a data-driven basis that is adaptive to the data instead of being determined a priori. The data-driven time-frequency method developed by this investigator and his colleagues has a solid mathematical foundation and uses a novel nonlinear optimization technique. Application of this method to the 9 year AMSU data over tropical oceans has led to the discovery of a new near-annual trend. This method has been applied to analyze blood pressure wave data, leading to a completely new way of diagnosing patients with cardiovascular diseases. The proposed method could provide a completely new way to analyze real world data. The proposed research will help train students and postdocs in this emerging research area. The knowledge, techniques and tools developed in this project will be disseminated through publishing in the open literature, and making available as open-source the software tools that are developed.

本文提出了一种新的数据驱动的时频分析方法来研究非线性和非平稳数据。其核心思想是使用非线性优化在尽可能大的字典上寻找信号的稀疏时频表示。这种方法的动机是物理应用和需要提取瞬时频率和趋势从多尺度数据产生的许多科学和工程应用。虽然已经引入了几种方法来从多尺度信号中提取瞬时频率，但这些方法受到各种限制，并且没有坚实的数学基础。由该研究者及其同事开发的数据驱动的时频分析方法提供了瞬时频率的数学严格定义。本文提出了一种基于L1正则化非线性最小二乘的非线性匹配追踪方法。该方法可用于提取信号的瞬时频率、瞬时趋势等有物理意义的信息。初步结果表明，该方法能够准确、高效地分解大范围的物理信号。将该方法应用于地球科学和生物医学应用中的一些真实的世界数据，得到了一些新的发现。该建议的主要目标之一是对该方法进行严格的收敛性研究，并将其应用于解决生物医学和地球科学应用中的一些具有挑战性的真实的世界问题。开发有效的数据分析方法是从海量数据中了解趋势、周期等隐藏模式的重要途径。到目前为止，大多数数据分析方法都使用预定的基础来处理数据。这些方法中的大多数只能处理线性和静态数据。为了更好地理解隐藏在数据中的物理机制，人们需要开发有效的方法来处理数据的非平稳性和非线性。这种方法需要使用一种数据驱动的基础，这种基础适应于数据，而不是事先确定的。由该研究者及其同事开发的数据驱动的时频方法具有坚实的数学基础，并使用了一种新颖的非线性优化技术。应用这种方法对9年的AMSU资料在热带海洋导致了一个新的近年度趋势的发现。该方法已被应用于分析血压波数据，导致一个全新的方式诊断患者的心血管疾病。该方法为分析真实的世界数据提供了一种全新的方法。拟议的研究将有助于培养学生和博士后在这个新兴的研究领域。将通过在公开文献中发表和将开发的软件工具作为开放源码提供，传播本项目开发的知识、技术和工具。