Skeletonization based on angle maps

This paper presents a novel skeleton pruning approach based on angle maps. The angle map of the test object is a representation of the object contour’s angles during a 2D empirical mode like decomposition (EMD-like). The intrinsic mode functions produced by the EMD like decomposition are used to compose the angle map of the object contour. This angle map has very good properties for obtaining the object’s skeleton. The experimental results demonstrate that the obtained skeletons match to hand-labelled skeletons provided by human subjects, even in the presence of significant noise and shape variations, cuts and tears, and have the same topology as the original skeletons.     

A HYBRID DEMAND FORECASTING MODEL BASED ON EMPIRICAL MODE DECOMPOSITION AND NEURAL NETWORK IN TFT-LCD INDUSTRY

Demand forecasting plays an important role in the thin-film transistor liquid crystal display (TFT-LCD) industry. A hybrid approach is proposed for demand forecasting by combining empirical mode decomposition (EMD) and neural networks. From the signal analysis point of view, demand can be considered as a nonlinear and nonstationary combination of different frequencies. Every demand can be represented by one or several frequencies. The process of the proposed approach first decomposes the historical demand data into a finite set of intrinsic mode functions (IMFs) and a residual through EMD. Then, these IMFs are input into a back-propagation neural network (BPN) and the corresponding demand is used to predict these IMFs. Finally, the demand is forecasted by summing the predicted IMFs. The results show that the proposed model outperforms the single BPN model without EMD preprocessing and the traditional autoregressive integrated moving average (ARIMA) models.     

基于NA-MEMD和互信息的脑电特征提取方法

多变量经验模式分解（MEMD）方法不需要根据先验知识选取基函数,能同时对多通道数据进行自适应分解,适合于分析具有高度相关性和非平稳性的脑电信号。为了判别包含有用信息的内蕴模式函数（IMFs）,提出一种基于噪声辅助多变量经验模式分解（NA-MEMD）和互信息的方法,并用于脑电特征提取。首先使用NA-MEMD算法对多通道信号进行分解得到多尺度IMF分量,然后采用互信息法分别计算各尺度上信号与其IMF分量、噪声与其IMF分量、信号IMF分量与噪声IMF分量之间的相关性,接着根据敏感因子筛选包含有用信息的IMF分量,将其叠加得到对应的重构信号,最后采用共同空间模式（CSP）法对重构信号进行特征提取,再用支持向量机（SVM）实现分类。使用仿真数据和实际数据集BCI Competition IV Data Set 1进行测试,与现有的其他方法比较,验证了所提方法的有效性。     

Nonlinear and adaptive undecimated hierarchical multiresolution analysis for real valued discrete time signals via empirical mode decomposition approach

Hierarchical multiresolution analysis is an important tool for the analysis of signals. Since this multiresolution representation provides a pyramid like framework for representing signals, it can extract signal information effectively via levels by levels. On the other hand, a signal can be nonlinearly and adaptively represented as a sum of intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD) algorithm. Nevertheless, as the IMFs are obtained only when the EMD algorithm converges, no further iterative sifting process will be performed directly when the EMD algorithm is applied to an IMF. As a result, the same IMF will be resulted and further level decompositions of the IMFs cannot be obtained directly by the EMD algorithm. In other words, the hierarchical multiresolution analysis cannot be performed via the EMD algorithm directly. This paper is to address this issue by performing a nonlinear and adaptive hierarchical multiresolution analysis based on the EMD algorithm via a frequency domain approach. In the beginning, an IMF is expressed in the frequency domain by applying discrete Fourier transform (DFT) to it. Next, zeros are inserted to the DFT sequence and a conjugate symmetric zero padded DFT sequence is obtained. Then, inverse discrete Fourier transform (IDFT) is applied to the zero padded DFT sequence and a new signal expressed in the time domain is obtained. Actually, the next level IMFs can be obtained by applying the EMD algorithm to this signal. However, the lengths of these next level IMFs are increased. To reduce these lengths, first DFT is applied to each next level IMF. Second, the DFT coefficients of each next level IMF at the positions where the zeros are inserted before are removed. Finally, by applying IDFT to the shorten DFT sequence of each next level IMF, the final set of next level IMFs are obtained. It is shown in this paper that the original IMF can be perfectly reconstructed. Moreover, computer numerical simulation results show that our proposed method can reach a component with less number of levels of decomposition compared to that of the conventional linear and nonadaptive wavelets and filter bank approaches. Also, as no filter is involved in our proposed method, there is no spectral leakage in various levels of decomposition introduced by our proposed method. Whereas there could be some significant leakage components in the various levels of decomposition introduced by the wavelets and filter bank approaches.     

Analysis of normal and epileptic seizure EEG signals using empirical mode decomposition

Epilepsy is one of the most common neurological disorders characterized by transient and unexpected electrical disturbance of the brain. The electroencephalogram (EEG) is an invaluable measurement for the purpose of assessing brain activities, containing information relating to the different physiological states of the brain. It is a very effective tool for understanding the complex dynamical behavior of the brain. This paper presents the application of empirical mode decomposition (EMD) for analysis of EEG signals. The EMD decomposes a EEG signal into a finite set of bandlimited signals termed intrinsic mode functions (IMFs). The Hilbert transformation of IMFs provides analytic signal representation of IMFs. The area measured from the trace of the analytic IMFs, which have circular form in the complex plane, has been used as a feature in order to discriminate normal EEG signals from the epileptic seizure EEG signals. It has been shown that the area measure of the IMFs has given good discrimination performance. Simulation results illustrate the effectiveness of the proposed method.     

基于EMD阈值算法的脉冲涡流信号消噪

针对脉冲涡流信号夹杂着较多的高频噪声,提出了一种新的经验模态分解阈值消噪算法。首先将信号分解为多个本征模态函数（Intrinsic Mode Function,IMF）,对信噪比低的高频IMF进行减小噪声能量处理后得到重组信号;再对重组信号进行EMD分解后根据白噪声统计特性对IMF筛选,对噪声含量多的IMF进行小波阈值消噪;最后将处理过的IMF与噪声含量少的IMF重构得到消噪后的信号。实验仿真的结果和数据表明,该方法可以减少失真,获得更高的信噪比,能够较好地消除噪声的干扰恢复出原始的信号。     

Skeleton pruning by contour partitioning with discrete curve evolution

In this paper, we introduce a new skeleton pruning method based on contour partitioning. Any contour partition can be used, but the partitions obtained by discrete curve evolution (DCE) yield excellent results. The theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable, even in the presence of significant noise and shape variations, and have the same topology as the original skeletons. In particular, we have proven that the proposed approach never produces spurious branches, which are common when using the known skeleton pruning methods. Moreover, the proposed pruning method does not displace the skeleton points. Consequently, all skeleton points are centers of maximal disks. Again, many existing methods displace skeleton points in order to produces pruned skeletons     

基于EMD多模态特征融合支持向量机的故障诊断

针对非平稳时间序列信号,提出一种基于经验模态分解(EMD)的特征提取和多模态特征融合支持向量机的故障诊断方法,首先对原始信号进行EMD分解,选择能量最大的几个基本模式分量(IMF)并提取其小波包特征,获得对每个IMF独立的特征子集;然后在每个IMF特征子集中训练SVM弱分类器,并根据各特征子集对应的IMF能量权重进行加权融合,获得故障状态的强分类器,将该方法应用于6135型柴油机振动信号故障诊断中,实验结果表明了其可行性和有效性.     

基于谱插值与经验模态分解的表面肌电信号降噪处理*

根据表面肌电(surface electromyography, sEMG)信号的噪声特性来探讨其降噪方法的应用问题。采用谱插值法来削弱工频干扰以避免工频处的肌电信息成分丢失,再选取通过经验模态分解(empirical mode decomposition, EMD)方法获得的内在模态函数(intrinsic mode function, IMF)分量作小波软阈值分析,并将部分明显的低频IMF干扰分量及冗余分量去除,然后对相应IMF分量进行重构便可得到降噪处理后的sEMG信号。仿真和真实信号的降噪实验结果     

Epileptic seizure classification in EEG signals using second-order difference plot of intrinsic mode functions

Epilepsy is a neurological disorder which is characterized by transient and unexpected electrical disturbance of the brain. The electroencephalogram (EEG) is a commonly used signal for detection of epileptic seizures. This paper presents a new method for classification of ictal and seizure-free EEG signals. The proposed method is based on the empirical mode decomposition (EMD) and the second-order difference plot (SODP). The EMD method decomposes an EEG signal into a set of symmetric and band-limited signals termed as intrinsic mode functions (IMFs). The SODP of IMFs provides elliptical structure. The 95% confidence ellipse area measured from the SODP of IMFs has been used as a feature in order to discriminate seizure-free EEG signals from the epileptic seizure EEG signals. The feature space obtained from the ellipse area parameters of two IMFs has been used for classification of ictal and seizure-free EEG signals using the artificial neural network (ANN) classifier. It has been shown that the feature space formed using ellipse area parameters of first and second IMFs has given good classification performance. Experimental results on EEG database available by the University of Bonn, Germany, are included to illustrate the effectiveness of the proposed method.     

基于奇异谱分析的经验模态分解去噪方法

提出了一种基于奇异谱分析(SSA)的经验模态分解(EMD)去噪方法。该方法先对带噪信号进行EMD分解,得到若干个本征模态函数(IMF)。再通过SSA对每个IMF分量进行去噪处理:把第一个IMF分量作为高频噪声,并根据它计算出剩余IMF中所含的噪声能量,从而得到剩下的每个IMF中信号所占的能量比值。然后选择合适的窗口长度,对每个IMF进行SSA变换,根据IMF中信号所占的能量比值选择合适的奇异值分解(SVD)分量重构,得到去噪后的IMF。再将所有重构得到的IMF分量以及余项相加,得到最终去噪后的信号。经过实验,对比研究了该方法与小波软阈值、EMD软阈值和EMD滤波方法的去噪效果,结果表明该方法整体优于其它方法,是一种有效的信号去噪方法。     

基于经验模式分解的时间序列数据流在线预测*

提出一种通用的时间序列数据流预测方法,算法首先通过经验模式分解方法将从链式重写窗口取得的数据集分解有限具有特征振荡周期的固有模态函数分量和一个代表原始序列平均趋势的余量;然后对于各个分量分别建立最大Lyapunov指数预测模型进行预测;最后将各分量的预测值组合获得最终预测值。通过电力负荷的预测实验表明,与单一的时间序列数据流预测模型相比,该模型具有较高的预测精度和很好的模型适应性。     

Partial ensemble approach to resolve the mode mixing of extreme-point weighted mode decomposition

Empirical mode decomposition (EMD) is an effective tool for breaking down components (modes) of a nonlinear and non-stationary signal. Recently, a newly adaptive signal decomposition method, namely extreme-point weighted mode decomposition (EWMD), was put forward to improve the performance of EMD, in particular, to resolve the over- or undershooting issue associated with the large amplitude variations. However, similar to EMD, EWMD also suffers the mode mixing problem caused by intermittence or noisy signals. In this paper, inspired by complementary ensemble EMD (CEEMD), a noise-assisted data analysis method called partial ensemble extreme-point weighted mode decomposition (PEEWMD) is proposed to eliminate the mode mixing problem and enhance the performance of EWMD. In the proposed PEEWMD method, firstly white noises in pairs are added to the targeted signal and then the noisy signals are decomposed using the EWMD method to obtain the intrinsic mode functions (IMFs) in the first several stages. Secondly, permutation entropy is employed to detect the components that cause mode mixing. The residual signal is obtained after the identified components are separated from the original signal. Lastly, the residual signal is fully decomposed by using the EWMD method. The proposed PEEWMD method is compared with original EWMD, ensemble EWMD (EEWMD) and CEEMD using simulated signals. The results demonstrate that PEEWMD can effectively restrain the mode mixing issue and generates IMFs with much better performance. Based on that the PEEWMD and envelope power spectrum based fault diagnosis method was proposed and applied to the rubbing fault identification of rotor system and the fault diagnosis of rolling bearing with inner race. The result indicates that the proposed method of fault diagnosis gets much better effect than EMD and EWMD.     

Electrocardiogram‐based emotion recognition system using empirical mode decomposition and discrete Fourier transform

Emotion recognition using physiological signals has gained momentum in the field of human computer–interaction. This work focuses on developing a user‐independent emotion recognition system that would classify five emotions (happiness, sadness, fear, surprise and disgust) and neutral state. The various stages such as design of emotion elicitation protocol, data acquisition, pre‐processing, feature extraction and classification are discussed. Emotional data were obtained from 30 undergraduate students by using emotional video clips. Power and entropy features were obtained in three ways – by decomposing and reconstructing the signal using empirical mode decomposition, by using a Hilbert–Huang transform and by applying a discrete Fourier transform to the intrinsic mode functions (IMFs). Statistical analysis using analysis of variance indicates significant differences among the six emotional states (p < 0.001). Classification results indicate that applying the discrete Fourier transform instead of the Hilbert transform to the IMFs provides comparatively better accuracy for all the six classes with an overall accuracy of 52%. Although the accuracy is less, it reveals the possibility of developing a system that could identify the six emotional states in a user‐independent manner using electrocardiogram signals. The accuracy of the system can be improved by investigating the power and entropy of the individual IMFs.     

Detrended fluctuation thresholding for empirical mode decomposition based denoising

Signal decompositions such as wavelet and Gabor transforms have successfully been applied in denoising problems. Empirical mode decomposition (EMD) is a recently proposed method to analyze non-linear and non-stationary time series and may be used for noise elimination. Similar to other decomposition based denoising approaches, EMD based denoising requires a reliable threshold to determine which oscillations called intrinsic mode functions (IMFs) are noise components or noise free signal components. Here, we propose a metric based on detrended fluctuation analysis (DFA) to define a robust threshold. The scaling exponent of DFA is an indicator of statistical self-affinity. In our study, it is used to determine a threshold region to eliminate the noisy IMFs. The proposed DFA threshold and denoising by DFA–EMD are tested on different synthetic and real signals at various signal to noise ratios (SNR). The results are promising especially at 0 dB when signal is corrupted by white Gaussian noise (WGN). The proposed method outperforms soft and hard wavelet threshold method.     

基于改进小波阈值-CEEMDAN算法的ECG信号去噪研究

Electrocardiogram (ECG) signal denoising has always been a hot research issue. In order to eliminate the noises in ECG signal, a denoising method based on adaptive complete set empirical mode decomposition (CEEMDAN) and wavelet improved threshold function is proposed. Firstly, this method firstly decomposes the ECG signal by CEEMDAN to obtain a set of intrinsic modal functions (IMFs) from high frequency to low frequency. CEEMDAN decomposition is performed on ECG signal to yield several modal components (IMF). Secondly, the correlation coefficient method is used to perform wavelet denoising with improved threshold on the high frequency IMFs. For the low frequency IMFs, by setting a fixed threshold, the IMFs below the threshold is considered to be the baseline drift signal and removed. Finally, the denoised IMFs and the retained IMFs are reconstructed. The experimental results show that the proposed method is more effective than the empirical mode decomposition (EMD) wavelet denoising, and the global average empirical mode decomposition (EEMD) wavelet denoising method.     

基于EMD和选择性集成学习算法的磨机负荷参数软测量

针对磨机筒体振动和振声信号组成复杂难以解释、蕴含信息存在冗余性和互补性、与磨机负 荷参数映射关系难以描述等问题,提出了基于经验模态分解（Empirical mode decomposition,EMD）技术和选择性集成学习算法分析 筒体振动与振声信号组成,建立磨机负荷参数软测量模型的新方法.首先从机理上定性分析了筒 体振动及振声信号组成的复杂性;然后采用EMD技术将原始信号自适应分解为具有不同时间尺度的系列组 成成分,即本征模态函数（Intrinsic mode function,IMF）;接着在频域内基于互信息（Mutual information,MI）方法分析并选择IMF频谱特征;最后采用基 于核偏最小二乘（Kernel partial least square,KPLS）建模方法、分支定界优化算法的选择性集成学习方法建立磨机负荷参数软测量模型,实现了多源多尺度频谱特征的选择性信息融合.基于实验球磨机的实际运行数据仿真验证了该方法的有效性.     

基于EEMD-RobustICA和Prony算法的谐波和间谐波检测方法

针对经验模态分解存在的模态混叠现象和Prony算法对噪声敏感的问题,将总体经验模态分解与鲁棒性独立分析法和Prony算法进行有机的结合,应用到谐波和间谐波的检测中。首先将含有噪声的谐波信号进行总体经验模态分解,得到不同阶数的固有模态函数,然后将其作为鲁棒性独立分量分析法的输入,对得到的独立分量进行软阈值去噪后进行逆变换得到重构后的固有模态函数,叠加得到去噪后的信号,最后用Prony算法对谐波和间谐波信号进行参数辨识,得到谐波和间谐波的参数。仿真结果表明,该方法具有较好的抗噪性,克服了Prony算法对噪声敏感的缺点,有效地提高了谐波和间谐波检测的精度。     

目标骨架的多尺度树表示

基于骨架的目标表示是计算机视觉领域的重要研究内容．虽然目前基于不同原理提出了许多骨架提取算法．但是关于利用骨架信息来有效地表示并识别目标的研究却很少．文章对骨架的结构基元自顶向下地进行分解,将基元组织成层次树表示．通过引入尺度的概念．获得了目标的节点数目小、连接关系稳定的多尺度树表示．实验表明，它可以紧致、稳健地表示目标，并可降低图匹配过程的复杂度．