局域波分析方法研究及其在心电信号处理中的应用
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摘要
局域波分析（Local WaveAnalysis, LWA）方法是一种基于信号局部特征的时频分析方法，适合分析、处理非线性、非平稳信号。经验模态分解（Empirical ModeDecomposition, EMD）是LWA方法的关键技术，EMD将复杂信号分解成有限个被称之为内蕴模式函数（Intrinsic Mode Function, IMF）的简单分量，进而可以计算得到有实际物理含义的瞬时频率（Instantaneous Frequency, IF）。本文主要对EMD等局域波分解方法进行了深入的研究，主要工作如下：
提出了两种包络拟合改进算法：基于最小长度约束分段三次Hermite插值（Least-length Constrained Piecewise Cubic Hermite Interpolation, LLC-PCHI）包络拟合方法和基于最平坦约束分段三次Hermite插值（Flattest Constrained Piecewise CubicHermite Interpolation, FC-PCHI）包络拟合方法。包络拟合是EMD方法的一个重要步骤，是决定EMD分解收敛速度与分解正确性的重要因素。本文提出的LLC-PCHI包络拟合方法以包络曲线长度最小为目标函数，采用Lagrange求极小值法优化极值点处的一阶导数值，然后采用分段三次Hermite插值方法进行包络拟合，得到平滑包络线；FC-PCHI包络拟合方法以拟合曲线的极值差最小作为目标函数，采用混沌粒子群优化算法优化极值点处的一阶导数，拟合出最平坦包络线。实验表明这两种方法均能有效地克服三次样条插值方法的过冲、欠冲现象和分段抛物线插值法的“弯折”现象，能拟合出更平滑的包络线，进而使得EMD分解得到的内蕴模式函数更准确，较好地克服模态混淆问题。
提出了根据信号的瞬时最小周期选择δ参数的方法，改进了一种基于偏微分方程的免插值EMD模型，尝试进行EMD的理论化研究。筛选过程是EMD的关键步骤，筛选过程研究的难点在于经典EMD关于“局部均值”的定义过于松散和模糊，不利于EMD的理论化研究，插值过程会引入与原信号无关的附加信息，从而导致筛选过程和所提取的IMFs严重依赖于所采用的插值方法，还会引起包络过冲、欠冲、端点效应等问题。为了避免筛选过程中的插值运算，本文推广了Diop等人提出的“局部均值算子”的成立范围；结合自伴Sturm-Liouville方程解的特点解释了δ IMF不但满足内蕴模式函数的条件之一——“局部均值为零”，而且满足内蕴模式函数的另一个条件——“极值点和过零点数量相等或者最多相差一个”；提出了根据信号的瞬时最小周期选择δ参数的方法，使得改进的基于偏微分方程EMD（Improved PartialDifferential Equation Based EMD，IPDE-Based EMD）模型适合分析非平稳信号。实验结果表明，IPDE-Based EMD方法不但能较好地克服经典EMD分解、FC-PCHI包络拟合EMD分解等方法中由于插值方法引起的端点效应问题，在一定程度上改善模态混淆问题，且由于δ参数的选择采用了基于信号本身特征的选择方法，能较好地解决Diop等人提出的基于偏微分方程的EMD模型不适用分析非带限信号的问题。
针对心电信号滤波预处理，提出了一种基于EMD方法的区域自适应硬阈值滤波算法。心电信号是一种典型的非平稳、微弱生物电信号，广泛应用于各种心脏疾病的诊断与治疗。心电信号中常伴有非常严重的高频、低频噪声，且噪声频带常与心电信号频带有重叠，滤波预处理较困难。本文结合自适应阈值方法，将EMD方法应用于心电信号的滤波预处理，在有效抑制高频、低频噪声的同时，能较好保留心电信号的主要特征波形。
利用EMD方法的自适应数据分析特性，提出了两种新的QRS综合波检测算法：基于EMD滤波和Hilbert变换的QRS综合波检测算法；基于IMF能量分布特点的QRS综合波检测算法。QRS综合波是心电信号中最显著的波群，QRS综合波的正确检测是心电信号自动分析系统的关键步骤。采用MIT-BIH Arrhythmia Database全部48个数据验证本文算法，平均正确检测率分别达99.78%和99.91%，表明这两种方法是高效的QRS综合波检测算法。
Local wave analysis (LWA) method is a recently developed time-frequency analysismethod, which is based on the local characteristics of the signal itself and thus can besuitable for non-linear and non-stationary signal analysis. Empirical mode decomposition(EMD) is one of the most important techniques of the LWA method. EMD methoddecomposes the complex signal into several basic components called intrinsic modefunctions (IMFs). Combined with the Hilbert transform, the real meaningful instantaneousfrequencies (IF) of the basic components can be calculated. Based on the in-depth studyand summarization to the previous researches, the local wave decomposition methodsrepresented by EMD are studied in this thesis. The main contributions are as follows:
Two new envelope fitting methods: the least-length constrained piecewise cubicHermite interpolation (LLC-PCHI) method and the flattest constrained piecewise cubicHermite interpolation method, are proposed. Envelope fitting is one of the important stepsof EMD. It is the key factor that determines EMD’s convergence rate and decompositioncorrectness. In the proposed LLC-PCHI method, taking the length of the fitted envelope asthe target function, Lagrange optimization method is used to optimize the derivatives of theinterpolation nodes. Then the piecewise cubic Hermite interpolation method with theoptimized derivatives is used to fit the more smooth envelopes. The proposed FC-PCHImethod effectively integrates the difference between extremes into the cost function, andapplies a chaos particle swarm optimization method to optimize the derivatives of theinterpolation nodes. The experimental results show that both the two methods caneffectively solve the overshoots and/or undershoots caused by CSI method and theartificial bends caused by piecewise parabola interpolation (PPI) method. Thecorresponding results of EMD can be more reasonable and accurate. Both the two methodscan improve the mode mixing problem well, which is one of the major drawbacks of theoriginal EMD.
A new scheme for the choice of parameter δ is proposed, which is based on the least instantaneous period of the signal. An improved partial differential equation based EMD(IPDE-Based EMD) is presented. Sifting process is the crucial part of EMD. It is difficultto study the principles of sifting process due to the loose and vague definition of “localmean”, which is adverse to the EMD’s theoretical framework. The interpolation procedurealways creates additional information that has nothing to do with the original signal. Andthe interpolation makes the sifting and the corresponding IMFs strongly relying on theinterpolants used. Moreover, the interpolation issue can cause the inherent problems duringthe sifting process such as overshoot, undershoot, end issue, etc. An interpolation-free localmean operator is proposed by Diop et al. The establishing scope of local mean operator isfurther promoted in the thesis. The δ IMFproposed by Diop only satisfies the “zerolocal mean” condition of IMF. In the thesis, combined with the properties of the solutionsof the self-adjoint Sturm-Liouville equations, the reason why δ IMFalso satisfies the“exactly one zero between any two successive local extrema” condition of IMF isexpounded, which is not mentioned in Diop’s previous works. A new scheme for the choiceof parameter δ based on the signal’s least instantaneous period is proposed, which makesthe proposed IPDE-Based EMD method be suitable for analysis of unlimited bandwidthsignal. The experimental results show that the proposed PDE-Based EMD can not onlyovercome the end issues caused by interpolations, but also improve the mode mixingproblem compared to the original EMD and the FC-PCHI EMD. Because of the newsignal-based selection of parameter δ, the IPDE-Based EMD is applicable to the unlimitedbandwidth signal analysis.
A novel EMD based on regional adaptive hard-threshold filtering algorithm forelectrocardiogram (ECG) signal is proposed. ECG signal is a kind of typical weak andnon-stationary bioelectric signals, which is widely used in the diagnosis and treatment ofmany heart diseases. ECG signal is easily contaminated by severe high frequency noisesuch as electromyographic interference and low frequency noise such as baseline wander.The frequency bands of noise and ECG signal are partially overlapped, which increases thedifficulty of ECG pre-processing. In the thesis, combined with the regional adaptivehard-threshold, the EMD method is applied to ECG pre-processing. The proposed methodcan not only effectively suppress the high frequency noise and low frequency noise butalso better keep the main features of the ECG waveforms.
Based on the adaptive property of EMD, a new QRS detector based on the EMD and Hilbert transform and another novel QRS detector based on the IMF’s energy distributionare presented. The QRS complex is the most striking waveform in ECG signal. Accuratedetermination of the QRS complex is crucial in computer-based ECG analysis. Theperformances of the proposed detectors are tested using all48records from MIT-BIHArrhythmia Database. The average correct detection rate is up to99.78%and99.91%respectively, which shows that both the two methods are efficient QRS detectors.
提出了两种包络拟合改进算法：基于最小长度约束分段三次Hermite插值（Least-length Constrained Piecewise Cubic Hermite Interpolation, LLC-PCHI）包络拟合方法和基于最平坦约束分段三次Hermite插值（Flattest Constrained Piecewise CubicHermite Interpolation, FC-PCHI）包络拟合方法。包络拟合是EMD方法的一个重要步骤，是决定EMD分解收敛速度与分解正确性的重要因素。本文提出的LLC-PCHI包络拟合方法以包络曲线长度最小为目标函数，采用Lagrange求极小值法优化极值点处的一阶导数值，然后采用分段三次Hermite插值方法进行包络拟合，得到平滑包络线；FC-PCHI包络拟合方法以拟合曲线的极值差最小作为目标函数，采用混沌粒子群优化算法优化极值点处的一阶导数，拟合出最平坦包络线。实验表明这两种方法均能有效地克服三次样条插值方法的过冲、欠冲现象和分段抛物线插值法的“弯折”现象，能拟合出更平滑的包络线，进而使得EMD分解得到的内蕴模式函数更准确，较好地克服模态混淆问题。
提出了根据信号的瞬时最小周期选择δ参数的方法，改进了一种基于偏微分方程的免插值EMD模型，尝试进行EMD的理论化研究。筛选过程是EMD的关键步骤，筛选过程研究的难点在于经典EMD关于“局部均值”的定义过于松散和模糊，不利于EMD的理论化研究，插值过程会引入与原信号无关的附加信息，从而导致筛选过程和所提取的IMFs严重依赖于所采用的插值方法，还会引起包络过冲、欠冲、端点效应等问题。为了避免筛选过程中的插值运算，本文推广了Diop等人提出的“局部均值算子”的成立范围；结合自伴Sturm-Liouville方程解的特点解释了δ IMF不但满足内蕴模式函数的条件之一——“局部均值为零”，而且满足内蕴模式函数的另一个条件——“极值点和过零点数量相等或者最多相差一个”；提出了根据信号的瞬时最小周期选择δ参数的方法，使得改进的基于偏微分方程EMD（Improved PartialDifferential Equation Based EMD，IPDE-Based EMD）模型适合分析非平稳信号。实验结果表明，IPDE-Based EMD方法不但能较好地克服经典EMD分解、FC-PCHI包络拟合EMD分解等方法中由于插值方法引起的端点效应问题，在一定程度上改善模态混淆问题，且由于δ参数的选择采用了基于信号本身特征的选择方法，能较好地解决Diop等人提出的基于偏微分方程的EMD模型不适用分析非带限信号的问题。
针对心电信号滤波预处理，提出了一种基于EMD方法的区域自适应硬阈值滤波算法。心电信号是一种典型的非平稳、微弱生物电信号，广泛应用于各种心脏疾病的诊断与治疗。心电信号中常伴有非常严重的高频、低频噪声，且噪声频带常与心电信号频带有重叠，滤波预处理较困难。本文结合自适应阈值方法，将EMD方法应用于心电信号的滤波预处理，在有效抑制高频、低频噪声的同时，能较好保留心电信号的主要特征波形。
利用EMD方法的自适应数据分析特性，提出了两种新的QRS综合波检测算法：基于EMD滤波和Hilbert变换的QRS综合波检测算法；基于IMF能量分布特点的QRS综合波检测算法。QRS综合波是心电信号中最显著的波群，QRS综合波的正确检测是心电信号自动分析系统的关键步骤。采用MIT-BIH Arrhythmia Database全部48个数据验证本文算法，平均正确检测率分别达99.78%和99.91%，表明这两种方法是高效的QRS综合波检测算法。
Local wave analysis (LWA) method is a recently developed time-frequency analysismethod, which is based on the local characteristics of the signal itself and thus can besuitable for non-linear and non-stationary signal analysis. Empirical mode decomposition(EMD) is one of the most important techniques of the LWA method. EMD methoddecomposes the complex signal into several basic components called intrinsic modefunctions (IMFs). Combined with the Hilbert transform, the real meaningful instantaneousfrequencies (IF) of the basic components can be calculated. Based on the in-depth studyand summarization to the previous researches, the local wave decomposition methodsrepresented by EMD are studied in this thesis. The main contributions are as follows:
Two new envelope fitting methods: the least-length constrained piecewise cubicHermite interpolation (LLC-PCHI) method and the flattest constrained piecewise cubicHermite interpolation method, are proposed. Envelope fitting is one of the important stepsof EMD. It is the key factor that determines EMD’s convergence rate and decompositioncorrectness. In the proposed LLC-PCHI method, taking the length of the fitted envelope asthe target function, Lagrange optimization method is used to optimize the derivatives of theinterpolation nodes. Then the piecewise cubic Hermite interpolation method with theoptimized derivatives is used to fit the more smooth envelopes. The proposed FC-PCHImethod effectively integrates the difference between extremes into the cost function, andapplies a chaos particle swarm optimization method to optimize the derivatives of theinterpolation nodes. The experimental results show that both the two methods caneffectively solve the overshoots and/or undershoots caused by CSI method and theartificial bends caused by piecewise parabola interpolation (PPI) method. Thecorresponding results of EMD can be more reasonable and accurate. Both the two methodscan improve the mode mixing problem well, which is one of the major drawbacks of theoriginal EMD.
A new scheme for the choice of parameter δ is proposed, which is based on the least instantaneous period of the signal. An improved partial differential equation based EMD(IPDE-Based EMD) is presented. Sifting process is the crucial part of EMD. It is difficultto study the principles of sifting process due to the loose and vague definition of “localmean”, which is adverse to the EMD’s theoretical framework. The interpolation procedurealways creates additional information that has nothing to do with the original signal. Andthe interpolation makes the sifting and the corresponding IMFs strongly relying on theinterpolants used. Moreover, the interpolation issue can cause the inherent problems duringthe sifting process such as overshoot, undershoot, end issue, etc. An interpolation-free localmean operator is proposed by Diop et al. The establishing scope of local mean operator isfurther promoted in the thesis. The δ IMFproposed by Diop only satisfies the “zerolocal mean” condition of IMF. In the thesis, combined with the properties of the solutionsof the self-adjoint Sturm-Liouville equations, the reason why δ IMFalso satisfies the“exactly one zero between any two successive local extrema” condition of IMF isexpounded, which is not mentioned in Diop’s previous works. A new scheme for the choiceof parameter δ based on the signal’s least instantaneous period is proposed, which makesthe proposed IPDE-Based EMD method be suitable for analysis of unlimited bandwidthsignal. The experimental results show that the proposed PDE-Based EMD can not onlyovercome the end issues caused by interpolations, but also improve the mode mixingproblem compared to the original EMD and the FC-PCHI EMD. Because of the newsignal-based selection of parameter δ, the IPDE-Based EMD is applicable to the unlimitedbandwidth signal analysis.
A novel EMD based on regional adaptive hard-threshold filtering algorithm forelectrocardiogram (ECG) signal is proposed. ECG signal is a kind of typical weak andnon-stationary bioelectric signals, which is widely used in the diagnosis and treatment ofmany heart diseases. ECG signal is easily contaminated by severe high frequency noisesuch as electromyographic interference and low frequency noise such as baseline wander.The frequency bands of noise and ECG signal are partially overlapped, which increases thedifficulty of ECG pre-processing. In the thesis, combined with the regional adaptivehard-threshold, the EMD method is applied to ECG pre-processing. The proposed methodcan not only effectively suppress the high frequency noise and low frequency noise butalso better keep the main features of the ECG waveforms.
Based on the adaptive property of EMD, a new QRS detector based on the EMD and Hilbert transform and another novel QRS detector based on the IMF’s energy distributionare presented. The QRS complex is the most striking waveform in ECG signal. Accuratedetermination of the QRS complex is crucial in computer-based ECG analysis. Theperformances of the proposed detectors are tested using all48records from MIT-BIHArrhythmia Database. The average correct detection rate is up to99.78%and99.91%respectively, which shows that both the two methods are efficient QRS detectors.
引文
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