An Approach to the Inverse Problem of Brain Functional Mapping Under the Assumption of Gamma Distributed Myogram Noise Within Rest Intervals Using the Independent Component Analysis*

Abstract

This paper is devoted to the challenging task of brain functional mapping, which is posed by current techniques of noninvasive human brain investigation. One of them is magnetoencephalography, which is potentially a very powerful tool for scientific and practical research. Big data, retrieved from magnetoencephalography procedure, comprise information about brain processes. MEG data processing sets a highly ill-posed problem of the spatial reconstruction of MEG signal sources with a given accuracy. At the moment there are no universal tools for solving this problem accurately enough. A similar distribution of measured potentials on the human head surface may reflect the magnetic activity of different areas within the cerebral cortex. Nevertheless, under certain assumptions this task can be solved unambiguously. These assumptions are: the discreteness of signal sources, originating from distinct functional brain areas, and the superficial location of the signal sources. The obtained MEG signals are assumed to be the superposition of multi-dipole signals. In this case the solution of the inverse problem is a multi-dipole approximation. A more precise model can be constructed under the assumption of the gamma distribution of myogram responses within rest intervals by developing relative associative filter. The proposed algorithm of inverse problem solution consists of two main steps. The first step includes the application of Independent component analysis to primary/basic MEG signals for the determination of independent components. At the second step these independent components are treated separately as monodipole models to get isolated signal source locations for each component.