Iterative Solvers for Inverse Bioelectric Field Problems

Internally funded project


Project Details

Project leader:
Prof. Dr. Ulrich Rüde


Contributing FAU Organisations:
Lehrstuhl für Informatik 10 (Systemsimulation)

Start date: 01/10/2001
End date: 30/09/2004


Abstract (technical / expert description):

Inverse problems are broadly characterized by their use of mathematical models for determining unknown system inputs, sources, parameters and/or states from observed system outputs and responses. This is the reverse of the typical, forward solution process wherein all system inputs, sources and parameters are known and mathematical models are used to predict the outputs and states.

An important class of inverse problems are those found in bioelectric field imaging. This model based analysis and visualization of bioelectric fields is of growing importance in the fields of Cardiology, Neurology and Neurosurgery. A characteristic of such problems is that because of the complex geometries, the number of degrees of freedom tends to be very large (on the order of millions) such that it is essential to create and use efficient solution techniques.

The aim of the project is to design new efficient solvers for these class of inverse problems. The research will be based on multilevel, conjugate gradient and row projection techniques. We plan to develop a mathematical analysis and to incorporate the algorithms into the SCIRun problem solving environment. SCIRun is a scientific programming environment that allows the interactive construction, debugging and steering of large-scale scientific computations. It will allow for testing the performance of the new algorithms on meshes generated from realistic patient MRI scans.


External Partners

University of Utah
Ovidius University of Constanta


Publications

Mohr, M., Popa, C., & Rüde, U. (2004). A Differential Inverse Problem from Cardiac Imaging. In Ion S, Marinoschi G, Popa C (Eds.), Mathematical Modelling of Environmental Life Sciences Problems (pp. 189--204). Constanta, Romania, RO: Bukarest: Editura Academiei Romane.
Mohr, M., Popa, C., & Rüde, U. (2004). An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices. International Journal of Computer Mathematics, 81(2), 215-226. https://dx.doi.org/10.1080/00207160310001650134
Mohr, M., & Roman, W. (2004). Cell-centred Multigrid Revisited. Computing and Visualization in Science, 7(3/4), 129-140. https://dx.doi.org/10.1007/s00791-004-0137-0
Mohr, M. (2004). Simulation of Bioelectric Fields: The Forward and Inverse Problem of Electro-encephalographic Source Analysis (Dissertation).
Mohr, M., Popa, C., & Rüde, U. (2003). An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices.
Mohr, M., & Vanrumste, B. (2003). Comparing Iterative Solvers for Linear Systems associated with the Finite Difference Discretisation of the Forward Problem in Electroencephalographic Source Analysis. Medical & Biological Engineering & Computing, 41(1), 75-84.
Popa, C., & Zdunek, R. (2003). Kaczmarz Extended Algorithm for Tomographical Image Reconstruction from Limited-Data.
Mohr, M., Popa, C., & Rüde, U. (2003). Numerical Solution of Least-Squares Problems by a Modified Kovarik Algorithm.
Pelican, E., & Popa, C. (2003). Some Remarks on a Collocation Method for First Kind Integral Equations.
Mohr, M., & Vanrumste, B. (2002). A Multigrid Solver in EEG Source Analysis applying the Finite Difference Method. International Journal of Bioelectromagnetism, 4(2), 255-256.

Last updated on 2019-19-03 at 11:16