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EN
Locating the sources of EEG signals (signal generators), i.e. indicating the places in the brain that the signals come from is the objective of the inverse problem in BCI applications using EEG. The two algorithms based on the methods used in the inverse problem: the linear least squares method and the LORETA1 method were compared. An analysis of the accuracy of locating the sources generating EEG signals on the basis of the two above mentioned methods was carried out with the use of the MATLAB programme. The findings made it possible to determine both the complexity of calculation involved in the methods under consideration and to compare the accuracy of the results obtained. Tests were done in which the inverse problem was solved on the basis of the data that were entered from the electrodes. Then potentials on electrodes were found by means of solving the forward problem once again ɸ (ɸ→ɸ). Moreover, tests were conducted on simulated data describing current density at selected places in the brain. In this case potentials on the electrodes were found by means of solving the forward problem. Subsequently the inverse problem was solved and potentials at selected places in the brain were specified J(J→Ĵ). In the case of J(J→Ĵ) only the relative error was examined, while the variance was studied in both cases. As a result of doing the tests, it was proved that relative errors were the same in the SVD and PINV methods, while in the LORETA method the error was similar. The variance computed for these methods was more differentiated for each of the cases, which made it possible to compare the algorithms in a better way. Differentiation of the variances under 0.2 shows that the algorithms that have been analyzed work properly. On the basis of knowing the results of the inverse problem, an attempt was made to make a selection of the best features of the EEG signal which differentiates the classes. In the present work tests were conducted to examine the differentiation of selected classes. Welch’s t-statistics was used to differentiate and order them. The results of the tests present the order for three classes of thought tasks, i.e. imagining moving one’s left hand, imagining moving one’s right hand, imagining generating words beginning with a randomly chosen letter. The present work is an introduction to a wider classification of features which are made with the use of inverse solutions.
EN
The article presents selected algorithms in inverse solutions in the EEG signal. When undertaking the calculations, it was assumed that the data obtained from electrodes on the surface of the head were preprocessed. As a result of using these algorithms it is possible to specify both the areas of the brain that the signals come from and the current density of the signals read by means of electrodes placed on the surface of the head. On the basis of knowing the solution to the inverse problem, an attempt was made to select the features of the signals. Then t-statistics was used to differentiate and order them.
PL
W artykule przedstawiono wybrane algorytmy rozwiązywania zagadnień odwrotnych w sygnale EEG. Przystępując do obliczeń założono, że dane uzyskane z elektrod rozmieszczonych na powierzchni głowy zostały wstępnie przetworzone. Wynikiem działania tych algorytmów jest lokalizacja obszarów mózgu, z których pochodzą sygnały oraz natężenia tych sygnałów odczytywanych za pomocą elektrod rozmieszczonych na powierzchni głowy. Znając rozwiązania zagadnienia odwrotnego podjęto też próbę selekcji cech. Wykorzystano t-statystykę do ich zróżnicowania i uszeregowania.
PL
Metody rejestrowania elektrycznych i magnetycznych aktywności mózgu jak elektroencefalografia (EEG) lub magnetoencefalografia (MEG) nie dają pełnej informacji o źródle rejestrowanych sygnałów. Przyjmując uproszczony model źródeł jako dipoli prądowych umieszczonych w różnych punktach mózgu, trzeba mieć na uwadze, że istnieje nieskończenie wiele różnych konfiguracji tych źródeł, które generują taki sam rozkład potencjałów na powierzchni czaszki. Przeprowadzane testy, w których porównywano wyniki poszukiwań źródeł aktywności, dały najlepsze wyniki dla metody LORETA, np. przedstawione w pracy Pascual-Marqui R. D.
EN
Methods of register electrical and magnetic brain activities as electroencephalography (EEG) or magnetoencefalography (MEG) do not give information about exact sources of registered signals. If is assumed a simplified model of sources as current dipole placed at different points of the brain, it should be taken into account that there are infinitely many different configurations of these sources which generate the same distribution of potentials on the surface of the skull. Tests carried out for solving the EEG inverse problem which compared the results of exploration activity sources gave the best results for the LORETA method, examples in paper Pascual- Marqui R. D.
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