经验模式分解的理论及其在磁共振波谱分析中的应用

项目名称： 经验模式分解的理论及其在磁共振波谱分析中的应用

项目编号： No.60873088

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 杨志华

作者单位： 广东财经大学

项目金额： 30万元

中文摘要： 经验模式分解（EMD）是一种自适应的数据分解方法。基于经验模式分解的Hilbert-Huang变换近年来获得了成功的应用。但是对整个HHT的基本理论，算法扩展以及面向某类具体问题的应用尚待完善。本项目针对这些问题展开了研究，已经取得的研究成果包括：（1）研究了周期解析信号的结构特征，发现解析信号是由两部分构成，在此基础上，进一步发现造成解析信号出现负的瞬时频率的原因与幅度有关，并给出了一类解析信号满足瞬时频率为正的条件。（2）指出固有模函数的两个条件并不独立，并对条件进行了修正；以此为基础，给出了二维固有模函数的模型，并提出了一种二维EMD算法。（3）对一维EMD算法进行了完善，提出了去骑波优先的EMD算法和基于拐点的EMD算法；提出用B样条来代替传统EMD中的平均包络，为建立EMD算法的数学表达提供了有益的探索。（4）建立了周期Bedrosian等式的时域充要条件，并构造了一类满足周期Bedrosian等式的周期解析信号，所构造的周期解析信号有非负的瞬时频率，并且在L p(T), 1 ≤p≤∞#26159;稠密的。（5）提出了基于EMD的若干应用，包括磁共振波谱信号的表示和信号特征检测等。

中文关键词： 经验模式分解（EMD）；Hilbert-Huang变换（HHT）；瞬时频率

英文摘要： Empirical mode decomposition is a novel method to adaptively analyze nonstationary data. Base on it, the Hilbert-Huang Transform(HHT) has been applied in many fields successfully. However, the theoretic foundation about the method has not been established. Some algorithms need to be improved, and the potential applications need further exploitation. This project focuses on these issues, some achievements have been made: (1)the constructions of period analytic signals have been studied. We found that an analytic signal consists of two parts, and a negative frequency in an analytic signal mainly derives from its amplitude. Furthermore, a class of conditions which keep instantaneous frequency of analytic signals positive have been established. (2) We have proved that Condition 1 of intrinsic mode function can really be decuced from Condition 2, then an improved definition of intrinsic mode function has been given. Based on it, a new model of the bidimensional intrinsic mode funtion has been founded. A novel bidimensional empirical mode decomposition algorithm has been developed by using Radon transform. (3) Some improvements about empirical mode decomposition algorithm have been made. The first remove ride wave EMD and an Oblique-extrema-based EMD have been developed. B-Spline analytical representation of the mean envelop for EMD has been presented. (4) Some new necessary and sufficient conditions for the circular Bedrosian identity have been established in time domain. A class of periodic analytic signals have been constructed, which have non-negative instantaneous frequency and are dense in L p(T), 1 ≤p≤∞ (5) Some applications based on EMD have successfully been exploited in many fields such as the time-frequency representation of Magnetic Resonance Spectroscopy and feature detection, texture classification, Iris recognition and signal denoising.

英文关键词： Empirical mode decomposition(EMD); Hilbert-Huang transform(HHT); Instantaneous frequency.