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.