Gastón Schlotthauer

A complete ensemble empirical mode decomposition with adaptive noise

In this paper an algorithm based on the ensemble empirical mode decomposition (EEMD) is presented. The key idea on the EEMD relies on averaging the modes obtained by EMD applied to several realizations of Gaussian white noise added to the original signal. The resulting decomposition solves the EMD mode mixing problem, however it introduces new ones. In the method here proposed, a particular noise is added at each stage of the decomposition and a unique residue is computed to obtain each mode. The resulting decomposition is complete, with a numerically negligible error. Two examples are presented: a discrete Dirac delta function and an electrocardiogram signal. The results show that, compared with EEMD, the new method here presented also provides a better spectral separation of the modes and a lesser number of sifting iterations is needed, reducing the computational cost.

Improved complete ensemble EMD: A suitable tool for biomedical signal processing

Abstract The empirical mode decomposition (EMD) decomposes non-stationary signals that may stem from nonlinear systems, in a local and fully data-driven manner. Noise-assisted versions have been proposed to alleviate the so-called “mode mixing” phenomenon, which may appear when real signals are analyzed. Among them, the complete ensemble EMD with adaptive noise (CEEMDAN) recovered the completeness property of EMD. In this work we present improvements on this last technique, obtaining components with less noise and more physical meaning. Artificial signals are analyzed to illustrate the capabilities of the new method. Finally, several real biomedical signals are decomposed, obtaining components that represent physiological phenomenons.

NOISE-ASSISTED EMD METHODS IN ACTION

In this work we explore the capabilities of two noise-assisted EMD methods: Ensemble EMD (EEMD) and the recently proposed Complete Ensemble EMD with Adaptive Noise (CEEMDAN), to recover a pure tone embedded in different kinds of noise, both stationary and nonstationary. Experiments are carried out for assessing their performances with respect to the level of the added noise and the number of realizations used for averaging. The obtained results partly support empirical recommendations reported in the literature while evidencing new distinctive features. While EEMD presents quite different behaviors for different situations, CEEMDAN evidences some robustness with an almost unaffected performance for the studied cases.

Screening of obstructive sleep apnea with empirical mode decomposition of pulse oximetry

Detection of desaturations on the pulse oximetry signal is of great importance for the diagnosis of sleep apneas. Using the counting of desaturations, an index can be built to help in the diagnosis of severe cases of obstructive sleep apnea-hypopnea syndrome. It is important to have automatic detection methods that allows the screening for this syndrome, reducing the need of the expensive polysomnography based studies. In this paper a novel recognition method based on the empirical mode decomposition of the pulse oximetry signal is proposed. The desaturations produce a very specific wave pattern that is extracted in the modes of the decomposition. Using this information, a detector based on properly selected thresholds and a set of simple rules is built. The oxygen desaturation index constructed from these detections produces a detector for obstructive sleep apnea-hypopnea syndrome with high sensitivity (0.838) and specificity (0.855) and yields better results than standard desaturation detection approaches.

A pattern recognition approach to spasmodic dysphonia and muscle tension dysphonia automatic classification.

Spasmodic dysphonia (SD) and muscle tension dysphonia (MTD) are two voice disorders that present similar characteristics. Usually, they can be differentiated only by experienced voice clinicians. There are many reasons that support the idea that SD is a neurological disease, requiring surgical treatments or, more usually, laryngeal botulinum toxin A injections as a therapeutic option. On the other hand, MTD is a functional disorder correctable with voice therapy. The importance of a correct diagnosis of these two disorders is critical at the treatment-selection moment. In this article, we present and compare the results of neural network and support vector machine-based methods that can help the clinicians to confirm their diagnosis. As a preliminary approach to the problem, we used only a sustained vowel /a/ to extract eight acoustic parameters. Then, a pattern recognition algorithm classifies the voice as normal, SD, or MTD. For comparison with previous works, we also separated the voices into normal and pathological (SD and MTD) voices with the methods proposed here. The results overcome the best classification rates between normal and pathological voices that have been previously reported, and demonstrate that our methods are very effective in distinguishing between MTD and SD.

An unconstrained optimization approach to empirical mode decomposition

Empirical mode decomposition (EMD) is an adaptive (data-driven) method to decompose non-linear and non-stationary signals into AM-FM components. Despite its well-known usefulness, one of the major EMD drawbacks is its lack of mathematical foundation, being defined as an algorithm output. In this paper we present an alternative formulation for the EMD method, based on unconstrained optimization. Unlike previous optimization-based efforts, our approach is simple, with an analytic solution, and its algorithm can be easily implemented. By making no explicit use of envelopes to find the local mean, possible inherent problems of the original EMD formulation (such as the under- and overshoot) are avoided. Classical EMD experiments with artificial signals overlapped in both time and frequency are revisited, and comparisons with other optimization-based approaches to EMD are made, showing advantages for our proposal both in recovering known components and computational times. A voice signal is decomposed by our method evidencing some advantages in comparison with traditional EMD and noise-assisted versions. The new method here introduced catches most flavors of the original EMD but with a more solid mathematical framework, which could lead to explore analytical properties of this technique. A new simple unconstrained optimization-based approach to EMD is introduced.The new method provides an analytical and easily implemented closed solution.Unlike other proposals, computational cost of the present one is similar to EMDs.The number of parameters to be tuned has been reduced to only one.The use of explicit spline interpolations is avoided.

Pathological voice analysis and classification based on empirical mode decomposition

Empirical mode decomposition (EMD) is an algorithm for signal analysis recently introduced by Huang. It is a completely data-driven non-linear method for the decomposition of a signal into AM - FM components. In this paper two new EMD-based methods for the analysis and classification of pathological voices are presented. They are applied to speech signals corresponding to real and simulated sustained vowels. We first introduce a method that allows the robust extraction of the fundamental frequency of sustained vowels. Its determination is crucial for pathological voice analysis and diagnosis. This new method is based on the ensemble empirical mode decomposition (EEMD) algorithm and its performance is compared with others from the state of the art. As a second EMD-based tool, we explore spectral properties of the intrinsic mode functions and apply them to the classification of normal and pathological sustained vowels. We show that just using a basic pattern classification algorithm, the selected spectral features of only three modes are enough to discriminate between normal and pathological voices.

Dimensionality reduction for visualization of normal and pathological speech data

For an adequate analysis of pathological speech signals, a sizeable number of parameters is required, such as those related to jitter, shimmer and noise content. Often this kind of high-dimensional signal representation is difficult to understand, even for expert voice therapists and physicians. Data visualization of a high-dimensional dataset can provide a useful first step in its exploratory data analysis, facilitating an understanding about its underlying structure. In the present paper, eight dimensionality reduction techniques, both classical and recent, are compared on speech data containing normal and pathological speech. A qualitative analysis of their dimensionality reduction capabilities is presented. The transformed data are also quantitatively evaluated, using classifiers, and it is found that it may be advantageous to perform the classification process on the transformed data, rather than on the original. These qualitative and quantitative analyses allow us to conclude that a nonlinear, supervised method, called kernel local Fisher discriminant analysis is superior for dimensionality reduction in the actual context.

Maximum approximate entropy and r threshold: A new approach for regularity changes detection

Approximate entropy (ApEn) has been widely used as an estimator of regularity in many scientific fields. It has proved to be a useful tool because of its ability to distinguish different system’s dynamics when there is only available short-length noisy data. Incorrect parameter selection (embedding dimension m, threshold r and data length N) and the presence of noise in the signal can undermine the ApEn discrimination capacity. In this work we show that rmax (ApEn(m,rmax,N)=ApEnmax) can also be used as a feature to discern between dynamics. Moreover, the combined use of ApEnmax and rmax allows a better discrimination capacity to be accomplished, even in the presence of noise. We conducted our studies using real physiological time series and simulated signals corresponding to both low- and high-dimensional systems. When ApEnmax is incapable of discerning between different dynamics because of the noise presence, our results suggest that rmax provides additional information that can be useful for classification purposes. Based on cross-validation tests, we conclude that, for short length noisy signals, the joint use of ApEnmax and rmax can significantly decrease the misclassification rate of a linear classifier in comparison with their isolated use.

Wavelet leader based multifractal analysis of heart rate variability during myocardial ischaemia

Heart rate variability is a non invasive and indirect measure of the autonomic control of the heart. Therefore, alterations to this control system caused by myocardial ischaemia are reflected in changes in the complex and irregular fluctuations of this signal. Multifractal analysis is a well suited tool for the analysis of this kind of fluctuations, since it gives a description of the singular behavior of a signal. Recently, a new approach for multifractal analysis was proposed, the wavelet leader based multifractal formalism, which shows remarkable improvements over previous methods. In order to characterize and detect ischaemic episodes, in this work we propose to perform a short-time windowed wavelet leader based multifractal analysis. Our results suggest that this new method provides appropriate indexes that could be used as a tool for the detection of myocardial ischaemia.