Simultaneous Random and Optimized Sources and Detectors for Efficient Optimization in Inverse Problems

Applied and Computational Mathematics Seminar
Monday, October 19, 2015 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Eric de Sturler – Department of Mathematics, Virginia Tech – sturler@vt.edu
Sung Ha Kang
In nonlinear inverse problems, we often optimize an objective function involving many sources, where each source requires the solution of a PDE. This leads to the solution of a very large number of large linear systems for each nonlinear function evaluation, and potentially additional systems (for detectors) to evaluate or approximate a Jacobian. We propose a combination of simultaneous random sources and detectors and optimized (for the problem) sources and detectors to drastically reduce the number of systems to be solved. We apply our approach to problems in diffuse optical tomography.This is joint work with Misha Kilmer and Selin Sariaydin.