Automatic Statistical Time-Frequency Analysis

自动统计时频分析

• 批准号: 6327454
• 负责人: WENSHENG GUO
• 金额: $ 26.17万
• 依托单位: UNIVERSITY OF PENNSYLVANIA
• 依托单位国家: 美国
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-02-01 至 2003-01-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/6327454
• 关键词: bioimaging /biomedical imaging; biomedical automation; brain disorder diagnosis; computer assisted diagnosis; electroencephalography; human data; mathematical model; method development; statistics /biometry; time resolved data

DESCRIPTION (provided by applicant): Non-stationary time series (i.e., time series with statistical properties that vary over time) arise in many areas of neuroscience research and clinical practice. For example, the spectral properties of electroencephalograms (EEGs) vary with brain state, and frequently this variation is of central clinical or scientific importance. Existing methods of spectra analysis assume that a time series is a realization of a stationary random process. These methods can be extended to non-stationary processes using windowed Fourier transforms, but the number and size of the windows must be chosen subjectively. We propose to develop improved, automatic statistical methods for analysis of non-stationary multivariate time series. We will evaluate the methods in applications to realistic simulated data and to real multi-channel EEG data required from patients with brain disorders. We will compare results from our automatic methods with the clinical judgments. Our specific aims are to develop, evaluate, apply, implement, and distribute the following statistical methods: (1) an estimator of the time-varying power spectrum of a univariate random process; (2) estimators of the time-varying spectral density matrix, coherences, and phase spectra of a multivariate random process; (3) time-frequency principal component analysis; (4) time-frequency filters; (5) cycle-spinning to reduce bias due to the dyadic structure of our estimators; and (6) univariate and multivariate processes that are smooth in both time and frequency domains. Our first proposed statistical methods are based on the Smooth Localized complex Exponential (SLEX) transform, which provides a rich selection of orthogonal transforms. The structure of the SLEX transform allows us to use the computationally efficient Best Basis algorithm of Coifman and Wickerhauser to automatically select a particular transform, which represents a segmentation of a non-stationary time series into approximately stationary intervals. Our second proposed approach (Aim 6) takes a new path. Unlike the traditional approaches that focus on modeling the Periodiograms, we propose to model the transfer function directly as a smooth function in both frequency and time using smoothing splines and to use a signal-plus-noise model. By modeling the transfer function directly, we alloy simultaneous smoothing in time and frequency within the Fourier transformation. Unlike the periodiogram, the transfer function preserves the phase information, and therefore the time-varying cross-spectra, coherence, and phase can be directly calculated from the transfer functions.

描述（申请人提供）：非平稳时间序列（即时间序列 统计特性随着时间而变化的系列在许多领域的许多领域出现 神经科学研究和临床实践。例如，光谱 脑电图（EEG）的特性随脑状态而变化，并且 这种变化通常具有核心临床或科学意义。 现有的光谱分析方法假定时间序列是实现 一个固定的随机过程。这些方法可以扩展到非平稳 使用窗口的傅立叶变换的过程，但是 必须主观选择窗口。我们建议开发改进的自动 非平稳多元时间序列分析的统计方法。我们 将评估应用程序中对现实的模拟数据的方法和 真正的多通道脑电图数据需要脑部疾病患者。我们 将将我们自动方法的结果与临床判断进行比较。 我们的具体目的是开发，评估，应用，实施和分发 以下统计方法： （1）单变量随机的时变功率谱的估计器 过程; （2）随时间变化的光谱密度矩阵的估计器， 相干和多元随机过程的相光谱； （3） 时频主成分分析； （4）时频过滤器； （5） 循环旋转以减少由于估计器的二元结构而减少偏差； （6）单变量和多变量过程，这些过程在时间和时间均光滑 频域。 我们提出的第一个统计方法基于平滑的本地化 复杂的指数（SLEX）变换，可提供丰富的选择 正交变换。 Slex变换的结构使我们能够使用 Coifman和Wickerhauser的计算有效的最佳基础算法 自动选择一个特定的转换，该转换代表 一个非平稳时间序列分为大约固定间隔。 我们提出的第二种方法（AIM 6）采取了新的道路。与传统不同 侧重于建模周期图的方法，我们建议建模 在频率和时间上直接传输功能作为平滑函数 使用平滑光环并使用信号加上噪声模型。通过建模 直接传输函数，我们合金同时平滑时， 傅立叶变换内的频率。与时期图不同， 传输函数保留了相位信息，因此 可以直接计算时变的跨光谱，连贯性和相位 从传输功能。