### Towards the Applications of Algorithms for Inverse Solutions in EEG Brain-Computer Interfaces

#### Abstract

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 Φ (Φ −Φ＾).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 −J＾). In the case of J(J −J＾) 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.

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