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Riemannian Manifold Informed Projections for Debiasing Multiple Data Covariance Matrices against Source Correlations

Student: Alisa Schepinova

Supervisor: Alexey Ossadtchi

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2020

Magnetoencephalography (MEG) is a neuroimaging method ideally suited for non-invasive studies of brain dynamics. MEG’s spatial resolution critically depends on the approach used to solve the ill-posed inverse problem in order to transform sensor signals into cortical activation maps. Over recent years non-globally optimized solutions based on the use of adaptive beamformers (BF) gained popularity. When operating in the environment with a small number of uncorrelated sources the BFs perform optimally and yield spatial super-resolution. However, the BFs are known to fail when dealing with correlated sources. In this paper we describe the new beamformer approach to deal with this problem. Namely, we refine the approach developed in "A. Kuznetsova, Y. Nurislamova, A. Ossadtchi, Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources". It preserves high spatial resolution in the environments with correlated sources. The method is based on a projection operation applied to the vectorized sensor-space covariance matrix. This projection does not remove the activity of the correlated sources from the sensor-space covariance matrix but rather selectively handles their contributions to the covariance matrix and creates a sufficiently accurate approximation of an ideal data covariance that could hypothetically be observed if these sources were uncorrelated.

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