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Mono-components vs IMFs in signal decomposition

INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 2008年第3期6卷 353-374页

作者： Qian, Tao Zhang, Liming Li, Hong Univ Macau Taipa Peoples R China Huazhong Univ Sci & Technol Wuhan 430074 Peoples R China

The concepts of intrinsic mode functions and mono-components are investigated in relation to the empirical mode decomposition. Mono-components are defined to be the functions for which non-negative analytic instantaneous frequency is well defined. We show that a great variety of functions are mono-components based on which adaptive decomposition of signals are theoretically possible. We justify the role of empirical mode decomposition in signal decomposition in relation to mono-components.

关键词： instantaneous frequency Hilbert transform mono-component empirical mode decomposition intrinsic mode functions Hilbert-Huang transform

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Bidimensional ensemble empirical mode decomposition of functional biomedical images taken during a contour integration task

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2014年第1期13卷 218-236页

作者： Al-Baddai, S. Al-Subari, K. Tome, A. M. Volberg, G. Hanslmayr, S. Hammwoehner, R. Lang, E. W. Univ Regensburg CIML Grp D-93040 Regensburg Germany Univ Regensburg D-93040 Regensburg Germany Univ Aveiro IEETA DETI P-3810 Aveiro Portugal Univ Konstanz Dept Psychol Cognit & Oscillat Lab Constance Germany

In cognitive neuroscience, extracting characteristic textures and features from functional imaging modalities which could be useful in identifying particular cognitive states across different conditions is still an important field of study. This paper explores the potential of two-dimensional ensemble empirical mode decomposition (2DEEMD) to extract such textures, so-called bidimensional intrinsic mode functions (BIMFs), of functional biomedical images, especially functional magnetic resonance images (fMRI) taken while performing a contour integration task. To identify most informative textures, i.e. BIMFs, a support vector machine (SVM) as well as a random forest (RF) classifier is trained for two different stimulus/response conditions. Classification performance is used to estimate the discriminative power of extracted BIMFs. The latter are then analyzed according to their spatial distribution of brain activations related with contour integration. Results distinctly show the participation of frontal brain areas in contour integration. Employing features generated from textures represented by BIMFs exhibit superior classification performance when compared with a canonical general linear model (GLM) analysis employing statistical parametric mapping (SPM). (C) 2014 Elsevier Ltd. All rights reserved.

关键词： intrinsic mode functions

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Autoregressive model-enhanced variational mode decomposition for mechanical fault detection

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2019年第6期13卷 843-851页

作者： Liu, Hui Xiang, Jiawei Wenzhou Univ Coll Mech & Elect Engn Wenzhou 325035 Peoples R China

Mechanical fault detection is an important research direction attracted a great attention. Variational mode decomposition (VMD) has been widely used due to the ability to generate in highly localised time-frequency (TF) representation. However, the method usually fails to analyse the non-stationary signal with the unknown low-frequency interferences. Combined with autoregressive (AR) model technique, an enhancement version of VMD method is proposed. First, VMD is employed to decompose the raw non-stationary vibration signal into a set of intrinsic mode functions (IMFs), which contain the faulty information, and the interference of high-frequency noises can be almost eliminated. Second, AR model is introduced to further purify each IMF through decreasing the interferences of unknown low-frequency components. Finally, Hilbert envelope analysis is applied to demodulate the purified signal and the fault can be determined by comparing the demodulation frequency with the theoretical faulty feature frequency. Numerical simulations and experimental investigations are conducted to validate the performance of the proposed method. The comparisons with two combinations, AR model and empirical mode decomposition (EMD), AR model and local mean decomposition (LMD) are given, and the comparative results verify the proposed method is superior to other methods for mechanical fault detection.

关键词： Hilbert transforms fault diagnosis demodulation signal denoising mechanical engineering computing vibrations condition monitoring autoregressive processes wavelet transforms IMF high-frequency noises AR model low-frequency components purified signal demodulation frequency theoretical faulty feature frequency local mean decomposition mechanical fault detection autoregressive model-enhanced variational mode decomposition important research direction highly localised time-frequency representation nonstationary signal low-frequency interferences autoregressive model technique enhancement version VMD method nonstationary vibration signal intrinsic mode functions

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Multi-kernel-based random vector functional link network with decomposed features for epileptic EEG signal classification

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IET SIGNAL PROCESSING 2020年第3期14卷 162-174页

作者： Parija, Sebamai Dash, Pradipta Kishore Bisoi, Ranjeeta Siksha O Anusandhan Univ Dept Elect & Commun Engn Bhubaneswar 751030 Odisha India Siksha O Anusandhan Univ Multidisciplinary Res Cell Bhubaneswar 751030 Odisha India

This study proposes an improved hybrid model built with empirical mode decomposition (EMD) features combined with weighted multi-kernel random vector functional link network (WMKRVFLN) where the kernel parameters are optimised with an efficient optimisation algorithm known as water cycle algorithm (WCA) for diagnosis and classification of epileptic electroencephalogram (EEG) signals. The proposed model with optimisation is known as WCA-EMD-WMKRVFLN. The tanh and wavelet kernel functions are contributing together to the effectiveness of the proposed model. The features generated from EMD in terms of intrinsic mode functions (IMFs) are modulated to find important statistical and entropy based features and these features in a reduced form are employed as inputs to the model to classify epileptic EEG signals. The presented approach is evaluated in terms of percentage correct classification accuracy (ACC), specificity and sensitivity using two datasets and is compared with different classifiers and state-of-the-art techniques. The highest accuracies of 99.69% (five-class) and 100% (three-class) achieved using the Bonn-University dataset and 99.0% ACC (two-class) achieved using the Bern-Barcelona dataset. The achieved results report that the presented approach is a promising approach for EEG signal classification and is superior to several state-of-the-art techniques and is highly comparable to many such techniques.

关键词： electroencephalography image classification signal classification support vector machines entropy wavelet transforms medical signal processing feature extraction optimisation epileptic EEG signals sensitivity multikernel-based random vector functional link network decomposed features epileptic EEG signal classification improved hybrid model empirical mode decomposition multikernel random vector functional link network kernel parameters efficient optimisation algorithm water cycle algorithm epileptic electroencephalogram signals WCA-EMD-WMKRVFLN kernel functions intrinsic mode functions important statistical based features entropy based features

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Fabric defect segmentation by bidimensional empirical mode decomposition

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TEXTILE RESEARCH JOURNAL 2014年第7期84卷 704-713页

作者： Li, Zhengxin Liu, Jianli Liu, Jihong Gao, Weidong Jiangnan Univ Key Lab ECO Text Wuxi 214122 Jiangsu Peoples R China

Fabric defect detection has attracted increasing attention in the fields of computer vision and textile engineering because it is essential to quality assurance of textile manufacturing. In this paper, we propose a novel defect detection scheme for fabric inspection based on bidimensional empirical mode decomposition. The stopping criterion for sifting and the intrinsic mode functions (IMFs) are adapted for this specific application. Appropriate IMFs are selected to eliminate influences of fabric textures and lighting in defect segmentation. The experiment results on sample images from our laboratory and from TILDA's Textile Texture Database demonstrate that the proposed method is a robust and accurate approach for fabric defect inspection.

关键词： intrinsic mode functions bidimensional empirical mode decomposition Defect detection

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FAST EMPIRICAL mode DECOMPOSITIONS OF MULTIVARIATE DATA BASED ON ADAPTIVE SPLINE-WAVELETS AND A GENERALIZATION OF THE HILBERT-HUANG-TRANSFORMATION (HHT) TO ARBITRARY SPACE DIMENSIONS

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ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS 2010年第3期2卷 337-358页

作者： Pabel, Roland Koch, Robin Jager, Gabriela Kunoth, Angela Univ Paderborn Inst Math Warburger Str 100 D-33098 Paderborn Germany

The Hilbert-Huang-Transform (HHT) has proven to be an appropriate multiscale analysis technique specifically for nonlinear and nonstationary time series on non-equidistant grids. It is empirically adapted to the data: first, an additive decomposition of the data (empirical mode decomposition, EMD) into certain multiscale components is computed, denoted as intrinsic mode functions. Second, to each of these components, the Hilbert transform is applied. The resulting Hilbert spectrum of the modes provides a localized time-frequency spectrum and instantaneous (time-dependent) frequencies. For the first step, the empirical decomposition of the data, a different method based on local means has been developed by Chen et al. (2006). In this paper, we extend their method to multivariate data sets in arbitrary space dimensions. We place special emphasis on deriving a method which is numerically fast also in higher dimensions. Our method works in a coarse-to-fine fashion and is based on adaptive (tensor-product) spline-wavelets. We provide some numerical comparisons to a method based on linear finite elements and one based on thin-plate-splines to demonstrate the performance of our method, both with respect to the quality of the approximation as well as the numerical efficiency. Second, for a generalization of the Hilbert transform to the multivariate case, we consider the Riesz transformation and an embedding into Clifford-algebra valued functions, from which instantaneous amplitudes, phases and orientations can be derived. We conclude with some numerical examples.

关键词： Multivariate data analysis arbitrary space dimension Hilbert-Huang-Transform (HHT) empirical mode decomposition (EMD) intrinsic mode functions (IMFs) tensor product spline wavelets adaptive wavelet-nD-EMD monogenic function Riesz transform Clifford algebra

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Signal analysis via instantaneous frequency estimation of signal components

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GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS 2015年第1期6卷 1-42页

作者： Chui, Charles K. van der Walt, Maria D. Stanford Univ Dept Stat Stanford CA 94305 USA Univ Missouri Dept Math & Comp Sci St Louis MO 63121 USA

The empirical mode decomposition (EMD) algorithm, introduced by Huang et al. (Proc Roy Soc Lond Ser A Math Phys Eng Sci 454(1971):903-995, 1998), is arguably the most popular mathematical scheme for non-stationary signal decomposition and analysis. The objective of EMD is to separate a given signal into a number of components, called intrinsic mode functions (IMF's) after which the instantaneous frequency (IF) and amplitude of each IMF are computed through Hilbert spectral analysis (HSA). On the other hand, the synchrosqueezed wavelet transform (SST), introduced by Daubechies and Maes (Wavelets in Medicine and Biology, pp. 527-546, 1996) and further developed by Daubechies et al. (Appl Comput Harmon Anal 30:243-261, 2011), is applied to estimate the IF's of all signal components of the given signal, based on one single reference "IF function", under the assumption that the signal components satisfy certain strict properties of a so-called adaptive harmonic model, before the signal components of the model are recovered. The objective of our paper is to develop a hybrid EMD-SST computational scheme by applying a "modified SST" to each IMF of the EMD, as an alternative approach to the original EMD-HSA method. While our modified SST assures non-negative instantaneous frequencies of the IMF's, application of the EMD scheme eliminates the dependence on a single reference IF value as well as the guessing work of the number of signal components in the original SST approach. Ourmodification of the SST consists of applying vanishing moment wavelets (introduced in a recent paper by C. K. Chui, Y.-T. Lin and H.-T. Wu) with stacked knots to process signals on bounded or half-infinite time intervals, and spline curve fitting with optimal smoothing parameter selection through generalized cross-validation. In addition, we formulate a local cubic spline interpolation scheme for real-time realization of the EMD sifting process that improves over the standard global cubic spline inter

关键词： Time-frequency analysis Instantaneous frequency Empirical mode decomposition intrinsic mode functions Synchrosqueezing wavelet transform Hilbert transform Hilbert spectrum Adaptive harmonic model Local spline interpolation

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Detection of focal electroencephalogram signals using higher-order moments in EMD-TKEO domain

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HEALTHCARE TECHNOLOGY LETTERS 2019年第3期6卷 64-69页

作者： Chatterjee, Soumya Jadavpur Univ Dept Elect Engn Kolkata 700032 India

Detection of epileptogenic focus based on electroencephalogram (EEG) signal screening is an important pre-surgical step to remove affected regions inside the human brain. Considering the fact above, in this work, a novel technique for detection of focal EEG signals is proposed using a combination of empirical mode decomposition (EMD) and Teager-Kaiser energy operator (TKEO). EEG signals belonging to focal (Fo) and non-focal (NFo) groups were at first decomposed into a set of intrinsic mode functions (IMFs) using EMD. Next, TKEO was applied on each IMF and two higher-order statistical moments namely skewness and kurtosis were extracted as features from TKEO of each IMF. The statistical significance of the selected features was evaluated using student's t-test and based on the statistical test, features from first three IMFs which show very high discriminative capability were selected as inputs to a support vector machine classifier for discrimination of Fo and NFo signals. It was observed that the classification accuracy of 92.65% is obtained in classifying EEG signals using a radial basis kernel function, which demonstrates the efficacy of proposed EMD-TKEO based feature extraction method for computer-based treatment of patients suffering from focal seizures.

关键词： brain support vector machines electroencephalography feature extraction medical signal processing medical disorders medical signal detection signal classification focal electroencephalogram signals higher-order moments EMD-TKEO domain epileptogenic focus electroencephalogram signal screening important pre-surgical step human brain empirical mode decomposition Teager-Kaiser energy operator nonfocal groups intrinsic mode functions IMF higher-order statistical moments focal seizures proposed EMD-TKEO based feature extraction method radial basis kernel function support vector machine classifier high discriminative capability statistical test statistical significance kurtosis skewness

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ENSEMBLE EMPIRICAL mode DECOMPOSITION AS AN ALTERNATIVE FOR TREE-RING CHRONOLOGY DEVELOPMENT

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TREE-RING RESEARCH 2018年第1期74卷 28-38页

作者： Guan, Biing T. Wright, William E. Cook, Edward R. Natl Taiwan Univ Sch Forestry & Resource Conservat Taipei 10617 Taiwan Univ Arizona Lab Tree Ring Res Tucson AZ 85721 USA Columbia Univ Lamont Doherty Earth Observ Tree Ring Lab Palisades NY 10964 USA

Since its establishment, tree-ring analysis has benefitted several scientific fields. Because of its many advantages, dendrochronology is a first choice to reconstruct past environmental variability. Two major concerns about the current tree-ring reconstruction paradigm are the subjective choices of detrending functions and the lack of fidelity to data of chronology generation methods. It is difficult to recover the original tree-ring data once they have been detrended and standardized. In this study, ensemble empirical mode decomposition (EEMD) is introduced as an objective high-fidelity stand-alone approach for developing tree-ring chronologies. Basic concepts of EEMD, recommended steps in developing chronologies, and available public domain programs are discussed. To demonstrate the potentials of EEMD for chronology development, two examples are provided, one for climate and the other for streamflow reconstructions. In both examples, EEMD chronologies show higher correlations with the instrumental data and have more power in their spectra than the ones developed based on the current tree-ring reconstruction approach. General usage concerns and cautions are also addressed.

关键词： empirical mode decomposition ensemble empirical mode decomposition intrinsic mode functions nonlinear and non-stationary time series

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Electrocardiograph compression based on sifting process of empirical mode decomposition

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ELECTRONICS LETTERS 2016年第9期52卷 688-689页

作者： Zhao, Chaojun Chen, Zhijian Meng, Jianyi Xiang, Xiaoyan Zhejiang Univ Inst VLSI Design Hangzhou 310027 Zhejiang Peoples R China Fudan Univ State Key Lab ASIC & Syst Shanghai 201203 Peoples R China

A new empirical mode decomposition (EMD)-based electrocardiograph (ECG) compressor is presented. Utilising the sifting process in EMD, the spline fitting function of the successive mean extrema together with the first intrinsic mode functions can perfectly reconstruct the ECG signal, the proposed method using the mean extrema for the compression. With optimal selection of the mean extrema and dead zone quantisation, and the application of run length coding and Huffman coding for further compression, the experimental results regarding several records of the MIT-BIH arrhythmia database shows that the proposed methods have a better compression results than recently developed ECG compressors.

关键词： splines (mathematics) electrocardiography signal reconstruction Huffman codes runlength codes medical signal processing electrocardiography compression sifting process empirical mode decomposition EMD-based ECG compressor spline fitting function intrinsic mode functions ECG signal reconstruction mean extrema zone quantisation run length coding Huffman coding MIT-BIH arrhythmia database

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