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PL
Literatura cyfrowego przetwarzania sygnałów jest zdominowana przez założenie o gaussowskim charakterze zakłóceń. Jednak w rzeczywistych warunkach zakłócenia charakteryzują się rozkładami innymi niż gaussowskie. Często zakłócenia mają charakter impulsowy. Z uwagi na dużą liczbę sygnałów elektrofizjologicznych, do badań został wybrany sygnał EKG. Podczas przeprowadzania prób wysiłkowych zakłócenia mięśniowe wykazują charakter impulsowy. Celem pracy jest przedstawienie różnych modeli zakłóceń impulsowych stosowanych do zakłócania sygnałów biomedycznych. W pracy zostaną przedstawione następujące modele zakłóceń: Gaussa-Bernoulliego, Gaussa-Laplace'a, Gaussa-Cauchy'ego oraz model wykorzystujący symetryczne rozkłady alfa-stabilne. Symulowane zakłócenia są dodawane do sygnału o zadanej wartości SNR. Następnie wykorzystując filtrację liniową oraz nieliniową zostaną zmierzone zniekształcenia resztowe w sygnale po filtracji.
EN
A literature of digital signal processing is dominated by the assumption of Gaussian distribution of disturbances. But in a real world of signals such statement is too optimistic. Some noises distributions differ from the idealistic Gaussian model. Noises are often impulsive in their nature. There exists many different electrophysiological signals, but for the purpose of this work the electrocardiogram (ECG signal) was chosen. This signal is almost always disturbed by a noise. A noise that appears in ECG signals during the stress test (mainly a muscle noise) has an impulsive nature. The main aim of this work is to present different models of an impulsive noise. In this paper the following models of impulsive disturbances are introduced: a Gaussian-Bernoulli, a Gaussian-Laplace, a Gaussian-Cauchy and a symmetric alpha-stable model. Simulated noise is added to signal with known values of SNR. Then the linear and nonlinear filtering methods are applied and the rest distortions in a filtered signal are measured.
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Content available remote The class of M-filters in the application of ECG signal processing
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EN
The main purpose of this paper is to present some advantages of nonlinear filtering of biomedical signals. The nonlinear M-filters are considered in this paper to suppress specific kind of noise - an impulsive noise in high resolution ECG signal. The impulsive noise can be modeled by symmetric \alfa-stable distribution (S\alfaS). The following type of M-filters are used in this work: median filter, myriad filter and five M-filter characterized by their cost function (skipped median, Andrew's sine, Tukey's biweight, standard M-filter, arc tangent M-filter). Their ability to suppress the impulsive noise is tested with a high resolution ECG signal that is corrupted by artificial noise and real muscle noise.
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EN
Robust filtering is a very promising area in application of biomedical signal processing. Signals are usually recorded with noise, which has various characteristics of baseline wander to very impulsive nature. The robust technique has been recently proposed as the tool to eliminate outliers in data samples. The main purpose of this paper is to present mean-median filters in application of ECG signal processing. The presented filter is evaluated in the presence of real muscle noise and simulated impulsive noise as a Gaussian-Laplace mixture. In order to suppress a noise with the best possible means, the special expression is proposed. The measure of distortions, which are introduced to a signal after operation of filtering, is estimated using the normalized mean square error. This factor is used to compare a quality of considered filters. Experimental results show improved performance according to the reference filters.
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EN
Biomedical signals are commonly recorded with many kinds of noise. One of these is a waveform of the electrical activity of muscles. This "natural" distortion is usually modelled with a white Gaussian noise. In order to suppress such noise a weighted myriad filter is applied. The weighted myriad filter belongs to a class of non-linear filters and requires knowledge about noise impulsiveness. An impulsive noise can be described with alpha-stable distributions. One objective of this paper is to apply alpha-stable distribution as a model of real-life muscle noise in ECG signals. The other objective of the paper is to apply a weighted myriad filter to suppress impulsive noise in biomedical (ECG) signals. The reference filters have been the Savitzky-Golay smoothing filter and the median filter. The obtained results have shown that alpha-stable distributions can be applied to model muscle noise and that a weighted myriad filter with a Chebyshev weighted function can effectively suppress such noise.
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Content available remote A new approach to robust, weighted signal averaging
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EN
In this paper, a new approach for robust, weighted averaging of time-aligned signals is proposed. Suppression of noise in such case can be achieved with the use of the averaging technique. The signals are time-aligned and then the average template is determined. To this end, the arithmetic mean operator is often applied to the synchronized signal samples or its various modifications. However, the disadvantage of the mean operator is its sensitivity to outliers. The weighted averaging operation can be regarded as special case of clustering. For that reason in this work the averaging process is formulated as the problem of certain criterion function minimization and a few different cost functions are employed. The maximum likelihood estimator of location based on the generalized Cauchy distribution is used as the cost function. Such approach allows to suppress various types of impulsive noise. The proposed methods performance is experimentally evaluated and compared to the reference methods using electrocardiographic signal in the presence of the impulsive noise and the real muscle noise as well as the case of noise power variations.
EN
The analysis of optokinetic nystagmus (OKN) provides valuable information about the condition of human vision system. One of the phenomena that is used in the medical diagnosis is optokinetic nystagmus. Nystagmus are voluntary or involuntarily eye movements being a response to a stimuli which activate the optokinetic systems. The electronystagmography (ENG) signal corresponding to the nystagmus has a form of a saw tooth waveform with fast components related to saccades. The accurate detection of the saccades in the ENG signal is the base for the further estimation of the nystagmus characteristic. The proposed algorithm is based on the proper filtering of the ENG signal providing a waveform with amplitude peaks corresponding the fast eyes rotation. The correct recognition of the local maxima of the signal is obtained by the means of fuzzy c-means clustering (FCM). The paper presents three variants of saccades detection algorithm based on the FCM. The performance of the procedures was investigated using the artificial as well as the real optokinetic nystagmus cycles. The proposed method provides high detection sensitivity and allows for the automatic and precise determination of the saccades location in the preprocessed ENG signal.
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EN
The analysis of eyes movements is a crucial part of eyes examination performed by clinicians. One of the characteristic type of eyes movements is a saccade. Its accurate detection is the base for further processing including the estimation of saccade parameters such as velocity, amplitude and duration. This paper presents averaging of optokinetic nystagmus (OKN) cycles that allows comparing and detecting different types of nystagmus phenomena. In order to average the OKN cycles the ENG signal needs to be processed. The saccade detection function is used to find the location of saccades in OKN waveform allowing the ENG signal to be divided into cycles. The resulting cycles are aligned using the Fourier shift method and then averaged providing the OKN cycle model, which can be used for evaluating the eyes at different movement conditions.
EN
The analysis of eye movements is valuable in both clinical work and research. One of the characteristic type of eye movements is saccade. The accurate detection of saccadic eye movements is the base for further processing of saccade parameters such velocity, amplitude and duration. This paper presents an accurate saccade detection method which is supported by the fuzzy clustering. The proposed detection function is computationally efficient and precisely determines the time position of the saccadic eye movement event. The described method is characterized by low sensitivity for any kind of noise and can be applied in the analysis of the congenital nystagmus.
EN
Averaging is one of the basic methods of statistical analysis of experimental data where the response of the system is periodic or quasi-periodic. As long as the noise are Gaussian, the standard averaging leads to good results and effective noise reduction. However, when the distortions have impulsive nature, then such an approach leads to a deterioration of the system. In this case the robust methods should be applied which are characterized by resistance to a statistical sample spoken. In this work a robust averaging method based on the minimization of a scalar criterion function using a Lp-norm functions are presented. The effectiveness of the proposed method was tested in an averaging periods aligned ECG signal cycles in the presence of impulse noise.
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PL
Sygnał elektrynystagmograficzny (ENG) z oczopląsem ma postać fali o piłokształtnym kształcie składającym się z fazy wolnej oraz szybkiej. Faza szybka to ruch sakkadyczny gałki ocznej. Skuteczna i dokładna detekcja sakkad ma kluczowe znaczenie w określeniu charakteru oczopląsu. W celu prawidłowej detekcji położenia sakkad sygnał ENG jest filtrowany a maksima lokalne są wykrywane za pomocą rozmytej metody c-średnich. Proponowany algorytm charakteryzuje się dużą czułością i pozwala na automatyczną i precyzyjną lokalizację sakkad w sygnale ENG.
EN
The electronystagmography (ENG) signal corresponding to nystagmus has a form of a saw tooth waveform with fast components related to saccades. The accurate detection of saccades in ENG signal is the base for the further estimation of the nystagmus characteristic. The proposed algorithm is based on the proper filtering of the ENG signal providing a waveform with amplitude peaks corresponding the fast eyes rotation. The correct recognition of the local maxima of the signal is obtained by the means of fuzzy c-means clustering (FCM). The proposed algorithm is highly sensitive and allows for the automatic and precise localization of the saccades in ENG signal.
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EN
Analysis of the fetal heart rate (FHR) signal is aimed at detection of clinically important patterns like bradycardia or tachycardia, accelerations and decelerations, as well as quantification of instantaneous FHR variability. Automated pattern recognition methods are based on estimation of so-called FHR baseline. It is a common opinion that the baseline estimation algorithm determines the efficiency of an entire process of quantitative signal analysis. Automated methods for baseline determination have been continuously improved for many years since there are still new classes of FHR signals being identified, for which the previous methods fail. The new method proposed for the baseline estimation is based on the weighted myriad filtering. The application of this method required filter parameter selection ensuring its operation according to clinical guidelines for baseline estimation. A very important feature of the myriad filtering is that there is no need for preliminary interpolation of signal loss segments. Our new algorithm was tested against two other methods. Thirty one-hour FHR recordings were selected for the analysis. Quantitative inconsistency was measured using differences between corresponding baseline samples. Additionally, the baselines were evaluated as regards their influence on identification of the acceleration and deceleration patterns. Obtained results allow us to conclude that the new algorithm delivers more reliable baselines particularly for signals with specific changes of the basal FHR level which has been recognized as difficult for baseline estimation.
EN
This paper addresses the problem of impulsive noise cancellation in digital signal area. The myriad and meridian filters are the type of robust filters which are very useful in suppressing the impulsive type of noise. The cost functions of theses filters have very similar structure. In this paper the generalized filter based on Lp norm is presented. The proposed filter operates in a wide range of impulsive noise due to the proper adjustment of p in the Lp norm. The presented filter is applied to suppress an impulsive noise in fetal heart rate (FHR) signal. Simulation results confirm the validity of the proposed filter.
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Content available An approach to unsupervised classification
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EN
Classification methods can be divided into supervised and unsupervised methods. The supervised classifier requires a training set for the classifier parameter estimation. In the case of absence of a training set, the popular classifiers (e.g. K-Nearest Neighbors) can not be used. The clustering methods are considered as unsupervised classification methods. This paper presents an idea of the unsupervised classification with the popular classifiers. The fuzzy clustering method is used to create a learning set. The learning set includes only these patterns that are the best representative of each class in the input dataset. The numerical experiment uses an artificial dataset as well as the medical datasets (PIMA, Wisconsin Breast Cancer) and illustrates the usefulness of the proposed method.
EN
The paper presents an unsupervised approach to biomedical signal segmentation. The proposed segmentation process consists of several stages. In the first step, a state-space of the signal is reconstructed. In the next step, the dimension of the reconstructed state-space is reduced by projection into principal axes. The final step involves fuzzy clustering method. The clustering process is applied in the kernel-feature space. In the experimental part, the fetal heart rate (FHR) signal is used. The FHR baseline and the acceleration or deceleration patterns are the main signal nonstationarities but also the most clinically important signal features determined and interpreted in computer-aided analysis.
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Content available Projective filtering based on L1-norm PC
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EN
The paper presents a modification of nonlinear state-space projections (NSSP) method. The proposed approach deals with the sub-space estimation problem. In the original NSSP method, the principal component analysis (PCA) is used for the subspace determination. The classical PCA uses L2-norm. It is well known that the L2-norm is sensitive to outliers. Thus, in this paper the L1-norm PCA is proposed a subspace determination. In numerical experiments an analytic signal and real ECG signals are processed with the proposed method. The signals are contaminated with Gaussian distributed noise with different signal to noise ratio (SNR). Obtained results confirm the usefulness of the proposed modification.
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