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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

Prognoza pogody jako forma pomiaru

Kozieł S.R.

Przegląd Geofizyczny

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2010

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Z. 1-2

37-48

PL

Niepewność prognozy pogody można traktować analogicznie jak niepewność pomiaru. Pomiaru dokonuje się za pomocą konkretnego przyrządu, któremu przypisana jest jego dokładność. W służbie hydrologiczno-meteorologicznej akt pomiaru jest jednorazowy. Pomiaru powtórzyć nie można, bo każdy następny będzie się odnosić do innego stanu środowiska. Podobnie każda metoda prognozy pogody stanowi swego rodzaju instrumentarium, za pomocą którego dokonuje się oceny stanu układu fizycznego w przyszłości. Metodę prognozy możemy potraktować jako swego rodzaju przyrząd służący do tak rozumianego pomiaru typu pośredniego. W praktyce, gdy dostępne są wyniki różnych modeli, powstaje problem łącznej interpretacji wyniku. Pokazano w pracy, że uwzględnienie w sposób racjonalny kilku wartości prognozowanych może mieć formę analogiczną do pomiaru fizycznego i polegać na ocenie konkretnej wielkości fizycznej kilkoma „przyrządami" o różnej dokładności. Dokładność prognozy każdego modelu z osobna jest zdefiniowana przez jego sprawdzalność. Jest to więc sytuacja analogiczna do problemu estymacji „wartości stałej", rozwiązanego i rozwiązywanego w praktyce metodą najmniejszych kwadratów, estymator BLUE. Uzyskano w ten sposób możliwość uśredniania wyników prognoz, gdy dla ustalonego punktu geograficznego i dla konkretnego momentu wyprzedzenia dostępne są wyniki modeli globalnych, mezoskalowych, lokalnych czy opracowanych przez synoptyka. Przedstawiona metoda uśredniania zbioru wartości prognozowanych sprowadza się do algorytmu średniej ważonej. Algorytm średniej ważonej może być stosowany również w sytuacji, gdy indywidualne prognozy są skorelowane, jak i w sytuacji gdy poszczególnym prognozom przypisuje się wagi subiektywne.

EN

It is possible to treat weather forecast uncertainty as uncertainty of measurements. The hydro-meteorological measurement is made by the definite device with known accuracy of the measurement. In hydro-meteorological practice the measurement is a single, unique action. It is not possible to repeat the measurement, because it would be made in different state of the environment. Every method of weather forecast may be considered as a result of some kind of measurement of the future system state - weather. Hence, every method of forecast may be treated as a kind of an indirect measurement device. In practice, when results of different models are available, some problems appear - how to interpret jointly their results. It is shown that for many simultaneous forecasts the applied procedure can be analogous to the procedure used when physical measurements consist of several values, like in a statistical sample. In practice forecast accuracy of every model is defined as a variance of forecasts error. So, the situation is analogous to the problem of „constant value" estimation, known in the BLUE theory. When individual forecasts are correlated the weighed averaging method can also be applied, as well as when it is attributed to subjective weight of individual forecasts.

4

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.