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1

Improved robust weighted averaging for event-related potentials in EEG

Kotowski Krzysztof, Stapor Katarzyna, Leski Jacek

Biocybernetics and Biomedical Engineering

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2019

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Vol. 39, no. 4

1036--1046

EN

The aim of this study was to improve the robust weighted averaging based on criterion function minimization and assess its effectiveness for extracting event-related brain potentials (ERP) from electroencephalographic (EEG) recordings. The areas of improvement include significantly lower averaging error (45% lower RMSE and 37% lower maximum difference than for original implementation) and increased robustness to local minima, strong outliers and corrupted epochs common to real-life EEG signals, especially from low-cost devices. Our proposed procedure was tested on two datasets, one artificially generated for purposes of this study (including different noise sources) and one real-life dataset collected with Emotiv EPOCþ. The lower error results mainly from more effective rejection (lowering the weights) of corrupted epochs by integrating the correlation-based weighting. The advantages of our method over pure correlation-based weighting are lower RMSE (up to two times) and robustness to the algorithm initialization and strong outliers. The performance of the methods was measured using bootstrap testing to avoid dependency of results on data. It shows that our improvements lead to significantly lower error, especially when the EEG signal is not filtered. The values of the parameters were adjusted for EEG signals but they can easily be incorporated in other repetitive electrophysiological measurement techniques.

2

A new approach to robust, weighted signal averaging

Pander T.

Biocybernetics and Biomedical Engineering

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2015

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Vol. 35, no. 4

317--327

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.

3

Porównanie metod ważonego uśredniania sygnału elektrokardiograficznego

Momot A.

Studia Informatica

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2012

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Vol. 33, nr 2A

567-580

PL

Ważone uśrednianie jest jedną z metod pozwalającą na redukcję poziomu zakłóceń w sygnałach o charakterze pseudocyklicznym, których przykładem jest sygnał EKG. Artykuł przedstawia kilka metod, w których do wyznaczania odpowiednich wag stosowany jest aparat analizy matematycznej oraz podejście statystyczne. Skuteczność działania tych metod przebadano dla zaszumionego sygnału ANE 20000.

EN

Weighted averaging is a method that allows to reduce the level of interference in the quasi-cyclic signals such as the ECG signal. This paper presents several methods, in which to determine the appropriate weights is used apparatus of mathematical analysis as well as the statistical approach. The performance of these methods were tested for the noisy signal ANE 20000.

4

Adaptacyjne podejście do tworzenia strategii inwestycyjnych na rynkach kapitałowych wraz z zastosowaniem ważonego uśredniania

Momot A., Momot M.

Studia Informatica

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2012

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Vol. 33, nr 2A

593-604

PL

Artykuł przedstawia propozycję projektowania strategii działania na rynkach kapitałowych, w szczególności na rynkach terminowych. Metoda polega na dwupoziomowej optymalizacji parametrycznej. Na drugim poziomie stosowana jest metoda ważonego uśredniania, gdzie dobór wag odbywa się na podstawie minimalizacji funkcjonału. Skuteczność przedstawionej metody została oceniona na podstawie bazy danych historycznych notowań kontraktów terminowych.

EN

This paper presents the design of strategy proposed for the capital markets, especially futures markets. The method is based on two-level parametric optimization. On the second level is used the weighted averaging method, where the choice of weights is based on the minimization of functional. The effectiveness of the method presented has been assessed based on historical data base of futures trading.

5

Filtering of two-dimensional digital images using weighted averaging for adaptive selection of weights

Momot A., Wrobel J., Horoba K., Jeżewski M., Bernys M.

Journal of Medical Informatics & Technologies

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2012

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Vol. 20

93--99

EN

Many digital images, especially in biomedical fields, contain some disturbances. The image analysis depends on quality of the images that is why reduction or elimination (if it is possible) the disturbances is the key issue. There are many methods of improvement in the quality of the images and thus improve the quality of the image analysis, among them one of the simplest method is low-pass filtering such as arithmetic mean or its generalization, weighted mean. The basic problem of the weighted mean is the proper selection of the weights. This can be done using adaptive algorithms. This paper presents several such algorithms which are modifications of the existing weighted averaging methods created originally for noise reduction in electrocardiographic signal. The description of the new filtering methods and a few results of its application are also presented with comparison to existing arithmetic average filtering.

6

Data partitioning based weighted averaging for noise suppression in biomedical signals

Momot A., Jezewski J., Wrobel J.

Journal of Medical Informatics & Technologies

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2012

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Vol. 20

85--91

EN

In the case of biomedical signals with a quasi-cyclic character, such as electrocardiographic signals, the high resolution electrocardiograms or electrical potentials recorded from the nervous system of patients (estimating brain activity evoked by a known stimulus), as a method of averaging in the time domain may be used for noise attenuation. In this paper there is presented input data partitioning applied to a few different methods of weighted averaging. This procedure usually leads to improve the quality of the resulting averaged signal, especially when fuzzy partitioning is used. Below it is presented the computational study of weighted averaging with traditional (sharp) and fuzzy partition of the input data in the presence of non-stationary noise. The performance of presented methods is experimentally evaluated for analytical signal of EN 60601-2-51 (2003), namely ANE20000 ECG record.

7

Zastosowanie ważonego uśredniania do projektowania strategii inwestycyjnych na rynkach kapitałowych

Momot A., Momot M.

Studia Informatica

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2011

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Vol. 32, nr 2A

473-483

PL

Metody inteligencji obliczeniowej są stosowane do projektowania strategii inwestycyjnych na rynkach kapitałowych. Jedną z takich metod jest ważone uśrednianie oparte na minimalizacji funkcji celu. Artykuł przedstawia przykład złożonej strategii inwestycyjnej, opartej na stosowaniu uśredniania wielu strategii elementarnych. Skuteczność przedstawionej metody została oceniona na podstawie bazy danych historycznych notowań kontraktów terminowych.

EN

Computational intelligence methods are used to design strategies in equity markets. Exemplary method is weighted averaging based on the minimization of objective function. This article presents a complex investment strategy based on the averaging of elementary strategies. Effectiveness of presented method was evaluated based on a database of futures tradings.

8

Ważone uśrednianie sygnału EKG wykorzystujące rozmyty podział sygnału oraz wnioskowanie Bayesowskie

Momot A.

Studia Informatica

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2009

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Vol. 30, nr 2A

287-297

PL

Akwizycja sygnału EKG wymaga tłumienia zakłóceń, co w przypadku sygnałów quasi-cyklicznych może być dokonywane przez ich uśrednianie. W warunkach rzeczywistych obserwuje się zmienność szumu z cyklu na cykl, co stanowi motywację dla stosowania metod ważonego uśredniania. W artykule proponuje się nową metodę uśredniania przy użyciu rozmytego podziału sygnału i bayesowskiego wnioskowania.

EN

cquisition of ECG signals needs noise attenuation which, in case of quasi-cyclic signals, may be made by means of averaging. In reality the variability of noise power from cycle to cycle is observed, which constitutes a motivation for using methods of weighted averaging. This paper proposes a new weighted method incorporating fuzzy partitioning of the signal and Bayesian inference.

9

Weighted averaging of ECG signals based on partition of input set in time domain

Momot A., Momot M., Łęski J.

Journal of Medical Informatics & Technologies

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2007

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Vol. 11

165--170

EN

The paper presents new approach to problem of signal averaging which is commonly used to extract a useful signal distorted by a noise. The averaging is especially useful for biomedical signal such as ECG signal, where the spectra of the signal and noise significantly overlap. In reality can be observed variability of noise power from cycle to cycle which is motivation for using methods of weighted averaging. Performance of the new method, based on partition of input set in time domain and criterion function minimization, is experimentally compared with the traditional averaging by using arithmetic mean, weighted averaging method based on empirical Bayesian approach and weighted averaging method based on criterion function minimization.

10

Bayesian and empirical Bayesian approach to weighted averaging of ECG signal

Mamot A., Mamot M., Łęski J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2007

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Vol. 55, nr 4

341-350

EN

One of the prime tool in non-invasive cardiac electrophysiology is the recording of an electrocardiographic signal (ECG) which analysis is greatly useful in the screening and diagnosis of cardiovascular diseases. However, one of the greatest problems is that usually recording an electrical activity of the heart is performed in the presence of noise. The paper presents Bayesian and empirical Bayesian approach to problem of weighted signal averaging in time domain which is commonly used to extract a useful signal distorted by a noise. The averaging is especially useful for biomedical signal such as ECG signal, where the spectra of the signal and noise significantly overlap. Using the methods of weighted averaging are motivated by variability of noise power from cycle to cycle, often observed in reality. It is demonstrated that exploiting a probabilistic Bayesian learning framework leads to accurate prediction models. Additionally, even in the presence of nuisance parameters the empirical Bayesian approach offers the method of theirs automatic estimation which reduces number of preset parameters. Performance of the new method is experimentally compared to the traditional averaging by using arithmetic mean and weighted averaging method based on criterion function minimization.

11

Historia rozwoju dwóch torfowisk mszarnych w Borach Tucholskich

Lamentowicz M., Obremska M., Mitchell Edward A.D.

Przegląd Geologiczny

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2006

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Vol. 54, nr 1

76-80

EN

Our research confirmed the value of kettle-hole mires for reconstructing Holocene environmental changes. The multi-proxy approach in which three palaeoecological methods were used (analyses of testate amoebae, plant macrofossils and pollen) improved the interpretation potential. We studied two Sphagnum mires situated in Tuchola Pinewoods (N Poland). In Tuchola mire 9000 years of environmental changes (groundwater level and pH) were recorded. Water table changes inferred from Tuchola mire show patterns similar to regional hydrological changes recorded in Polish lakes and mires as well as in other European sites. Jelenia Wyspa mire recorded changes in local vegetation and palaeohydrology during the last 1500 years. A rise in the groundwater table, caused by deforestation in the catchment area, allowed Sphagnum to expand. Consequently, the peatland evolved into an oligotrophic mire dominated by peat mosses. Approx. 200 years ago water pH increased and subsequently decreased, the lowest value being associated with the deforestation maximum. Furthermore, the planting of pine probably also caused an acidification of Jelenia Wyspa mire.

12

Empirical Bayesian averaging method and its application to noise reduction in ECG signal

Momot A., Momot M., Łęski J.

Journal of Medical Informatics & Technologies

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2006

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Vol. 10

93--101

EN

An electrocardiogram (ECG) is the prime tool in non-invasive cardiac electrophysiology and has a prime function in the screening and diagnosis of cardiovascular diseases. However one of the greatest problems is that usually recording an electrical activity of the heart is performed in the presence of noise. The paper presents empirical Bayesian approach to problem of signal averaging which is commonly used to extract a useful signal distorted by a noise. The averaging is especially useful for biomedical signal such as ECG signal, where the spectra of the signal and noise significantly overlap. In reality the variability of noise can be observed, with power from cycle to cycle, which is motivation for weighted averaging methods usage. It is demonstrated that by exploiting a probabilistic Bayesian learning framework, it can be derived accurate prediction models offering significant additional advantage, namely automatic estimation of 'nuisance' parameters. Performance of the new method is experimentally compared to the traditional averaging by using arithmetic mean and weighted averaging method based on criterion function minimization.