Boundary Integral Methods for Computing Covariances in Inverse Source Problems
Paul Beckman, New York University
When incorporating noisy experimental data into computational models of scattering from engineered objects, uncertainty in the specified incoming wave can lead to error in the resulting scattered field. We consider this inverse source problem, in which the geometry of the scatterer is known, and we wish to construct a statistical model for the boundary data. Using spectral and layer potential representations of the solution, we derive rapidly converging series for the resulting covariance of the scattered field.
Abstract Author(s): Paul G. Beckman, Michael O'Neil