OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

"Numerics for inverse problems in biomedical imaging"
Wolfgang Bangerth (Texas A&M University, USA)

In many of the modern biomedical imaging modalities, the measurable signal
can be described as the solution of a partial differential equation that
depends nonlinearly on the tissue properties (the "parameters") one would
like to image. Consequently, there are typically no explicit solution
formulas for these so-called "inverse problems" that can recover the
parameters from the measurements, and the only way to generate body images
from measurements is through numerical approximation.

The resulting parameter estimation schemes have the underlying partial
differential equations as side-constraints, and the solution of these
optimization problems often requires solving the partial differential
equation thousands or hundred of thousands of times. The development of
efficient schemes is therefore of great interest for the practical use of
such imaging modalities in clinical settings.

In this talk, the formulation and efficient solution strategies for such
inverse problems will be discussed, and we will demonstrate its efficacy
using examples from our work on Optical Tomography, a novel way of imaging
tumors in humans and animals. The talk will conclude with an outlook on
even more complex problems that attempt to automatically optimize
experimental setups to obtain better images.

This seminar is part of a workshop on "PDE Optimization and Inverse Problems", more information.