A Bayesian inverse solution using independent component analysis

Abstract

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.

Independent components analysis (ICA) at the “cocktail-party” in analytical chemistry

“…Similarly, a Genetic ICA algorithm was introduced as the feature extraction method to improve the prediction accuracy of the Back-propagation neural network method for the simultaneous determination of four exchangeable cations (K + , Na + , Ca 2+ and Mg 2+ ) to monitor the irrigation water quality [67]. The ICA mixing matrix has also been used as an input to obtain a Bayesian posterior for a spatial source distribution [68].…”