A Bayesian inverse solution using independent component analysis.
We present new results about the simultaneous linear inverse problems using independent component analysis (ICA), which can be used to separate the data into statistically independent components. The idea of using ICA in solving such inverse problems, especially in EEG/MEG context, has been a known topic for at least more than a decade, but the known results have been justified heuristically, and their relationships are not understood properly. Here we show how to obtain a Bayesian posterior for a spatial source distribution, by using an ICA demixing matrix as an input. The posterior enables us to rederive and reinterpret the previously known methods, and also provides completely new methods.
Department of Mathematics and Statistics, University of Helsinki, Finland; Department of Computer Science and HIIT, University of Helsinki, Finland.
Jouni
J
Puuronen
Department of Mathematics and Statistics, University of Helsinki, Finland; Department of Computer Science and HIIT, University of Helsinki, Finland. Electronic address: aapo.hyvarinen@helsinki.fi.
Aapo
A
Hyvärinen
D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain; D003198:Computer Simulation; D004569:Electroencephalography; D006801:Humans; D015225:Magnetoencephalography; D008962:Models, Theoretical; D025341:Principal Component Analysis
Bayesian methods; Electroencephalography; Independent component analysis; Inverse problem; Magnetoencephalography; Source localization