Sarah Leweke,
Volker Michel
S. 153 - 192
doi:
10.1553/etna_vol57s153
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol57s153
Abstract:
Reconstruction of the neuronal current inside the human brain from non-invasive measurements of the magnetic flux density via magnetoencephalography (MEG) or of electric potential differences via electroencephalography (EEG) is an invaluable tool for neuroscientific research, as it provides measures of activity in the brain. However, it is also a severely ill-posed inverse problem. Assuming spherical geometries, we consider the spherical multiple-shell model for the inverse MEG and EEG problem and apply the regularized functional matching pursuit algorithm (RFMP) for its solution. We present a new convergence proof for the RFMP for operators between two infinite-dimensional Hilbert spaces. Moreover, we utilize the complementarity of EEG and MEG data to combine inversions of simultaneous electric and magnetic measurements. Finally, we test the algorithm numerically on synthetic data using several Sobolev norms as penalty term and apply it to real data.
electroencephalography, greedy algorithms, ill-posed problems, integral equation, inverse problems, magnetoencephalography, regularization methods, regularized functional matching pursuit, Sobolev spaces
Published Online:
2022/09/19 12:49:18
Object Identifier:
0xc1aa5576 0x003db145
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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