Computational methods in electromagnetic biomedical inverse problems
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Doctoral thesis (article-based)
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Date
2008
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Language
en
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Verkkokirja (746 KB, 40 s.)
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Research reports / Helsinki University of Technology, Institute of Mathematics
A,
560
Abstract
This work concerns computational methods in electromagnetic biomedical inverse problems. The following biomedical imaging modalities are studied: electro/magnetoencephalography (EEG/MEG), electrical impedance tomography (EIT), and limited-angle computerized tomography (limited-angle CT). The use of a priori information about the unknown feature is necessary for finding an adequate answer to an inverse problem. Both classical regularization techniques and Bayesian methodology are applied to utilize the a priori knowledge. The inverse problems specifically considered in this work include determination of relatively small electric conductivity anomalies in EIT, dipole-like sources in EEG/MEG, and multiscale X-ray absorbing structures in limited-angle CT. Computational methods and techniques applied for solving these have been designed case-by-case. Results concern, among others, appropriate parametrization of inverse problems; two-stage reconstruction processes, in which a region of interest (ROI) is determined in the first stage and the actual reconstruction is found in the second stage; effective forward simulation through h- and p- versions of the finite element method (FEM); localization of dipole-like electric sources through hierarchical Bayesian models; implementation of the Kirsch factorization method for reconstruction of conductivity anomalies; as well as the use of a coarse-to-fine reconstruction strategy in linear inverse problems.Description
Keywords
inverse problems, electromagnetics, biomedical imaging, electroencephalography (EEG), electrical impedance tomography (EIT), limited-angle computerized tomography (limited angle CT), regularization, Bayesian methodology, Markov chain Monte Carlo (MCMC), factorization method of Kirsch, forward modeling and simulation, h-FEM, p-FEM, magnetoencephalography (MEG)
Other note
Parts
- [Publication 1]: Sampsa Pursiainen. 2006. Two-stage reconstruction of a circular anomaly in electrical impedance tomography. Inverse Problems, volume 22, number 5, pages 1689-1703. © 2006 Institute of Physics Publishing. By permission.
- [Publication 2]: S. Pursiainen and H. Hakula. 2006. A high-order finite element method for electrical impedance tomography. PIERS Online, volume 2, number 3, pages 260-264. © 2006 The Electromagnetics Academy (TEA). By permission.
- [Publication 3]: Nuutti Hyvönen, Harri Hakula, and Sampsa Pursiainen. 2007. Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography. Inverse Problems and Imaging, volume 1, number 2, pages 299-317. © 2007 American Institute of Mathematical Sciences (AIMS). By permission.
- [Publication 4]: Sampsa Pursiainen. 2008. EEG/MEG forward simulation through h- and p-type finite elements. Journal of Physics: Conference Series, volume 124, number 1, 012041, 11 pages. © 2008 Institute of Physics Publishing. By permission.
- [Publication 5]: Daniela Calvetti, Harri Hakula, Sampsa Pursiainen, and Erkki Somersalo. 2008. Conditionally Gaussian hypermodels for cerebral source localization. arXiv:0811.3185v1 [math-ph].
- [Publication 6]: Sampsa Pursiainen. 2008. Coarse-to-fine reconstruction in linear inverse problems with application to limited-angle computerized tomography. Journal of Inverse and Ill-Posed Problems, volume 16, number 9, pages 873-886.