Internally funded project
Start date : 01.10.2001
End date : 30.09.2004
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.
Funded by NATO