Back to Departmental Colloquium: Spring 2016
Departmental Colloquium
Date: Thursday, Feb 4, 2016
Time: 4:00PM
Location: LCB 219
Francois Monard
University of Michigan, Ann Arbor
Title |
Toward imaging modalities with high(er) resolution |
Abstract |
Given an unknown physical quantity to be imaged, the extent to which an imaging approach best exploits the mathematics and physics of the problem highly impacts (i) what can be reconstructed, and (ii) the available resolution of the resulting images. Improvements in both directions are of tremendous interest for medical applications, for example, and can be achieved by changing the underlying inverse problem into another one displaying better invertibility and conditioning. We will illustrate this strategy by discussing the mathematical analysis of inverse problems associated with two models. The first is the Boltzmann transport equation, a model for Optical Tomography and Single Photon Emission Computerized Tomography. The second is a class of elliptic partial differential equations with internal measurements, motivated by coupled-physics (or hybrid) medical imaging. In this context, the analysis of some models concerned with the reconstruction of conductivity and elasticity tensors has shown manifest improvements in both resolution and the capability of accessing previously unavailable anisotropic features. |
Differential Equations
Computational Mathematics