Processing of laser Doppler flowmetry signals from healthy subjects and patients with varicose veins: information categorization approach based on intrinsic mode functions and entropy computation

International audience

The multiscale entropy algorithm and its variants: a review

International audience

Analysing the similarity of proteins based on a new approach to empirical mode decomposition

The function of a protein can be partially determined by the information contained in its amino acid sequence. It can be assumed that proteins with similar amino acid sequences normally have closer functions. Hence analysing the similarity of proteins has become one of the most important areas of protein study. In this work, a layered comparison method is used to analyze the similarity of proteins. It is based on the empirical mode decomposition (EMD) method, and protein sequences are characterized by the intrinsic mode functions (IMFs). The similarity of proteins is studied with a new cross-correlation formula. It seems that the EMD method can be used to detect the functional relationship of two proteins. This kind of similarity method is a complement of traditional sequence similarity approaches which focus on the alignment of amino acids

EMG signal filtering based on Empirical Mode Decomposition

This paper introduces a procedure for filtering electromyographic (EMG) signals. Its key element is the Empirical Mode Decomposition, a novel digital signal processing technique that can decompose my time-series into a set of functions designated as intrinsic mode functions. The procedure for EMG signal filtering is compared to a related approach based on the wavelet transform. Results obtained from the analysis of synthetic and experimental EMG signals show that Our method can be Successfully and easily applied in practice to attenuation of background activity in EMG signals. (c) 2006 Elsevier Ltd. All rights reserved.

Empirical mode decomposition: a novel technique for the study of tremor time series

Tremor is a clinical feature characterized by oscillations of a part of the body. The detection and study of tremor is an important step in investigations seeking to explain underlying control strategies of the central nervous system under natural (or physiological) and pathological conditions. It is well established that tremorous activity is composed of deterministic and stochastic components. For this reason, the use of digital signal processing techniques (DSP) which take into account the nonlinearity and nonstationarity of such signals may bring new information into the signal analysis which is often obscured by traditional linear techniques (e.g. Fourier analysis). In this context, this paper introduces the application of the empirical mode decomposition (EMD) and Hilbert spectrum (HS), which are relatively new DSP techniques for the analysis of nonlinear and nonstationary time-series, for the study of tremor. Our results, obtained from the analysis of experimental signals collected from 31 patients with different neurological conditions, showed that the EMD could automatically decompose acquired signals into basic components, called intrinsic mode functions (IMFs), representing tremorous and voluntary activity. The identification of a physical meaning for IMFs in the context of tremor analysis suggests an alternative and new way of detecting tremorous activity. These results may be relevant for those applications requiring automatic detection of tremor. Furthermore, the energy of IMFs was visualized as a function of time and frequency by means of the HS. This analysis showed that the variation of energy of tremorous and voluntary activity could be distinguished and characterized on the HS. Such results may be relevant for those applications aiming to identify neurological disorders. In general, both the HS and EMD demonstrated to be very useful to perform objective analysis of any kind of tremor and can therefore be potentially used to perform functional assessment.

Use of intrinsic modes in biology: Examples of indicial response of pulmonary blood pressure to ± step hypoxia

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero “local mean,” and a final nonoscillatory mode. With this device, we obtain a set of “mean trends,” each of which represents a “mean” in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of “indicial response function” is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.

Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

多尺度分解与相位反褶积提高海上地震资料分辨率和信噪比

Offshore seismic exploration is full of high investment and risk. And there are many problems, such as multiple. The technology of high resolution and high S/N ratio on marine seismic data processing is becoming an important project. In this paper, the technology of multi-scale decomposition on both prestack and poststack seismic data based on wavelet and Hilbert-Huang transform and the theory of phase deconvolution is proposed by analysis of marine seismic exploration, investigation and study of literatures, and integration of current mainstream and emerging technology. Related algorithms are studied. The Pyramid algorithm of decomposition and reconstruction had been given by the Mallat algorithm of discrete wavelet transform In this paper, it is introduced into seismic data processing, the validity is shown by test with field data. The main idea of Hilbert-Huang transform is the empirical mode decomposition with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions that admit well-behaved Hilbert transform. After the decomposition, a analytical signal is constructed by Hilbert transform, from which the instantaneous frequency and amplitude can be obtained. And then, Hilbert spectrum. This decomposition method is adaptive and highly efficient. Since the decomposition is based on the local characteristics of the time scale of data, it is applicable to nonlinear and non-stationary processes. The phenomenons of fitting overshoot and undershoot and end swings are analyzed in Hilbert-Huang transform. And these phenomenons are eliminated by effective method which is studied in the paper. The technology of multi-scale decomposition on both prestack and poststack seismic data can realize the amplitude preserved processing, enhance the seismic data resolution greatly, and overcome the problem that different frequency components can not restore amplitude properly uniformly in the conventional method. The method of phase deconvolution, which has overcome the minimum phase limitation in traditional deconvolution, approached the base fact well that the seismic wavelet is phase mixed in practical application. And a more reliable result will be given by this method. In the applied research, the high resolution relative amplitude preserved processing result has been obtained by careful analysis and research with the application of the methods mentioned above in seismic data processing in four different target areas of China Sea. Finally, a set of processing flow and method system was formed in the paper, which has been carried on in the application in the actual production process and has made the good progress and the huge economic benefit.

中高层大气对低层大气声重波响应的分析

Acoustic Gravity waves (AGW) play an important role in balancing the atmospheric energy and momentum budget. Propagation of gravity wave in the atmosphere is one of the important factors of changing middle and upper atmosphere and ionosphere. The purpose of this dissertation is to study the propagation of gravity wave in a compression atmosphere whit means of numerical simulation and to analyze the response of middle and upper atmosphere to pulse disturbance from lower atmosphere. This work begins with the establishment of 2-D fully nonlinear compressible atmospheric dynamic model in polar coordinate, which is used ton numerically study gravity wave propagation. Then the propagation characteristics of acoustic gravity wave packets are investigated and discussed. We also simulate the response of middle and upper atmosphere to pulse disturbance of lower atmosphere in background winds or without background winds by using this model and analyze the data we obtained by using Fourier Transform (FT), Short-time Fourier Transform (STFT) and Empirical Mode Decomposition (EMD) method which is an important part of Hilbert-Huang Transform (HHT). The research content is summarized in the following: 1. By using a two-dimensional full-implicit-continuous-Eulerian (FICE) scheme and taking the atmospheric basic motion equations as the governing equations, a numerical model for nonlinear propagation of acoustic gravity wave disturbance in two-dimensional polar coordinates is solved. 2. Then the propagation characteristics of acoustic gravity wave packets are investigated and discussed. Results of numerical simulation show that the acoustic gravity wave packets propagate steadily upward and keep its shape well after several periods. 3. We simulate the response of middle and upper atmosphere to pulse disturbance of lower atmosphere in background winds or without background winds by using this model, and obtain the distribution of a certain physical quantity in time and space from earth’s surface to 300km above. The results reveal that the response of ionosphere occurs at a large horizontal distance from the source and the disturbance becomes greater with increasing of height. The situation when the direction of the background wind is opposite to or the same as the direction of disturbed velocity of gravity-wave is studied. The results show that gravity wave propagating against winds is easier than those propagating along winds and the background wind can accelerate gravity wave propagation. Just upon the source, an acoustic wave component with period of 6 min can be found. These images of simulation are similar to observations of the total electron content (TEC) disturbances caused by the great Sumatra-Andaman earthquake on December 26 in 2004. 4. Using the EMD method the disturbed velocity data of a certain physical quantity in time and space can be decomposed into a series of intrinsic mode function (IMF) and a trend mode respectively. The results of EMD reveal impact of the gravity wave frequency under the background winds.

HHT在电磁信号处理中的应用

In modem signal Processing，non－linear，non－Gaussian and non－stable signals are usually the analyzed and Processed objects，especially non－stable signals. The convention always to analyze and Process non－stable signals are： short time Fourier transform，Wigner－Ville distribution，wavelet Transform and so on. But the above three algorithms are all based on Fourier Transform，so they all have the shortcoming of Fourier Analysis and cannot get rid of the localization of it. Hilbert－Huang Transform is a new non－stable signal processing technology，proposed by N. E. Huang in 1998. It is composed of Empirical Mode Decomposition (referred to as EMD) and Hilbert Spectral Analysis (referred to as HSA). After EMD Processing，any non－stable signal will be decomposed to a series of data sequences with different scales. Each sequence is called an Intrinsic Mode Function (referred to as IMF). And then the energy distribution plots of the original non－stable signal can be found by summing all the Hilbert spectrums of each IMF. In essence，this algorithm makes the non－stable signals become stable and decomposes the fluctuations and tendencies of different scales by degrees and at last describes the frequency components with instantaneous frequency and energy instead of the total frequency and energy in Fourier Spectral Analysis. In this case，the shortcoming of using many fake harmonic waves to describe non－linear and non－stable signals in Fourier Transform can be avoided. This Paper researches in the following parts： Firstly，This paper introduce the history and development of HHT，subsequently the characters and main issues of HHT. This paper briefly introduced the basic realization principles and algorithms of Hilbert－Huang transformation and confirms its validity by simulations. Secondly, This paper discuss on some shortcoming of HHT. By using FFT interpolation, we solve the problem of IMF instability and instantaneous frequency undulate which are caused by the insufficiency of sampling rate. As to the bound effect caused by the limitation of envelop algorithm of HHT, we use the wave characteristic matching method, and have good result. Thirdly, This paper do some deeply research on the application of HHT in electromagnetism signals processing. Based on the analysis of actual data examples, we discussed its application in electromagnetism signals processing and noise suppression. Using empirical mode decomposition method and multi-scale filter characteristics can effectively analyze the noise distribution of electromagnetism signal and suppress interference processing and information interpretability. It has been founded that selecting electromagnetism signal sessions using Hilbert time-frequency energy spectrum is helpful to improve signal quality and enhance the quality of data.

Independent component analysis of climate data: A new look at EOF rotation

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.

Atenuação de ruídos coerentes utilizando decomposição em modos empíricos

The seismic processing technique has the main objective to provide adequate picture of geological structures from subsurface of sedimentary basins. Among the key steps of this process is the enhancement of seismic reflections by filtering unwanted signals, called seismic noise, the improvement of signals of interest and the application of imaging procedures. The seismic noise may appear random or coherent. This dissertation will present a technique to attenuate coherent noise, such as ground roll and multiple reflections, based on Empirical Mode Decomposition method. This method will be applied to decompose the seismic trace into Intrinsic Mode Functions. These functions have the properties of being symmetric, with local mean equals zero and the same number of zero-crossing and extremes. The developed technique was tested on synthetic and real data, and the results were considered encouraging

Sparse time-frequency data analysis : a multi-scale approach

In this work, we further extend the recently developed adaptive data analysis method, the Sparse Time-Frequency Representation (STFR) method. This method is based on the assumption that many physical signals inherently contain AM-FM representations. We propose a sparse optimization method to extract the AM-FM representations of such signals. We prove the convergence of the method for periodic signals under certain assumptions and provide practical algorithms specifically for the non-periodic STFR, which extends the method to tackle problems that former STFR methods could not handle, including stability to noise and non-periodic data analysis. This is a significant improvement since many adaptive and non-adaptive signal processing methods are not fully capable of handling non-periodic signals. Moreover, we propose a new STFR algorithm to study intrawave signals with strong frequency modulation and analyze the convergence of this new algorithm for periodic signals. Such signals have previously remained a bottleneck for all signal processing methods. Furthermore, we propose a modified version of STFR that facilitates the extraction of intrawaves that have overlaping frequency content. We show that the STFR methods can be applied to the realm of dynamical systems and cardiovascular signals. In particular, we present a simplified and modified version of the STFR algorithm that is potentially useful for the diagnosis of some cardiovascular diseases. We further explain some preliminary work on the nature of Intrinsic Mode Functions (IMFs) and how they can have different representations in different phase coordinates. This analysis shows that the uncertainty principle is fundamental to all oscillating signals.

Atenuação de ruídos coerentes utilizando decomposição em modos empíricos

The seismic processing technique has the main objective to provide adequate picture of geological structures from subsurface of sedimentary basins. Among the key steps of this process is the enhancement of seismic reflections by filtering unwanted signals, called seismic noise, the improvement of signals of interest and the application of imaging procedures. The seismic noise may appear random or coherent. This dissertation will present a technique to attenuate coherent noise, such as ground roll and multiple reflections, based on Empirical Mode Decomposition method. This method will be applied to decompose the seismic trace into Intrinsic Mode Functions. These functions have the properties of being symmetric, with local mean equals zero and the same number of zero-crossing and extremes. The developed technique was tested on synthetic and real data, and the results were considered encouraging