Studies on Signals and Images via the Fourier Transform

通过傅里叶变换研究信号和图像

• 批准号: 1513647
• 负责人: Suhasini Subba Rao
• 金额: $ 18.43万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-15 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1513647&HistoricalAwards=false
• 关键词: Studies; Signals; Images; via; Fourier

The goal of this project is to develop novel statistical methods that address some of the current challenges in analyzing spatio-temporal data frequently encountered in neuroimaging. One major application of this project is to identify features in brain signals that could differentiate healthy individuals from patients with neurological or mental diseases. The second application is to identify changes that take place in a brain signal during cognitive processing (e.g., while a human learns a new motor skill or while a rat learns risks and rewards in a controlled experiment). The third application is to identify biomarkers in brain signals that could predict a stroke patient's ability to recover loss of motor functionality. The approach used to solve these problems requires a study of the oscillatory patterns in these brain signals. Motivated by these practical problems, statistical methods based on the discrete Fourier transform (DFT) are developed. The DFT gives an indication of the decomposition of variance in the time series. Under stationarity, the covariance of the DFT is sparse and thus a departure from sparsity is an indication of non-stationarity. Moreover, the covariance of the DFT can be utilized as a discriminator between classes of signals. Using the properties of the DFT, novel methods for (1) change-point detection in time series based on sparsity of the DFT, and (2) discrimination and classification of classes of time series based on the properties of the covariance of the DFT will be developed. The DFT will also be used to estimate the variance of functionals of the spectrum and test for serial correlation and stationarity in nonlinear time series. Validation for stationary spatial processes and non-stationary spatial processes using the two-dimensional DFT will also be developed.

该项目的目标是开发新的统计方法，解决目前在分析神经影像学中经常遇到的时空数据方面的一些挑战。该项目的一个主要应用是识别大脑信号中的特征，这些特征可以将健康个体与神经系统或精神疾病患者区分开来。第二个应用是识别在认知处理期间大脑信号中发生的变化（例如，当人类学习新的运动技能时，或者当大鼠在受控实验中学习风险和回报时）。 第三个应用是识别大脑信号中的生物标志物，这些生物标志物可以预测中风患者恢复运动功能丧失的能力。 解决这些问题的方法需要研究这些大脑信号的振荡模式。 受这些实际问题的启发，发展了基于离散傅里叶变换（DFT）的统计方法。DFT给出了时间序列中方差分解的指示。在平稳性下，DFT的协方差是稀疏的，因此偏离稀疏性是非平稳性的指示。 此外，DFT的协方差可以用作信号类别之间的协方差。 利用DFT的性质，将开发用于（1）基于DFT的稀疏性的时间序列中的变点检测和（2）基于DFT的协方差的性质的时间序列类别的鉴别和分类的新方法。 DFT还将用于估计谱的泛函的方差，并测试非线性时间序列中的序列相关性和平稳性。 还将开发使用二维DFT的固定空间过程和非固定空间过程的验证。