Joint Seminar
Statistical Engineering Division/Physics

Seungseok Oh
Purdue University
Room 152, Nist North
September 27, 2004, 10:30-11:30 AM

Optical Diffusion Tomography (ODT) is a method for determining volumetric maps of optical absorption and scattering properties from measurements of light intensity transmitted through a highly scattering medium. While ODT holds great potential as a safe, non-invasive medical diagnostic modality with chemical specificity, it presents a difficult nonlinear inverse problem since the forward model is described by solutions to partial differential equations.

In this talk, we discuss Bayesian methods for the inversion of ODT problems, and we present a novel nonlinear multigrid inversion algorithm for solving the resulting nonquadratic optimization problems. The multigrid inversion algorithm works directly in an optimization framework by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. The resulting solution minimizes a cost functional that trades off accurate fitting of the data with smoothness or regularity of the solution. An application of our multigrid inversion method to ODT shows the potential for very large computational savings and robust convergence.