Variational Methods for Dynamic Inverse Problems in the Life Sciences

Non-FAU Project


Project Details

Project leader:
Prof. Dr. Martin Burger


Contributing FAU Organisations:
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Funding source: Europäische Union (EU) (EU FP 7 - ERC Consolidator Grants)
Acronym: LifeInverse
Start date: 01/03/2014
End date: 28/02/2019


Short description (intelligible to all):

This project will develop novel techniques for solving inverse problems in
life sciences, in particular related to dynamic imaging. Major challenges in
this area are efficient four- dimensional image reconstruction under low SNR
conditions and further the quantification of image series as obtained from
molecular imaging or life microscopy techniques. We will tackle both of them in
a rather unified framework as inverse problems for time-dependent (systems of)
partial differential equations.

In the solution of these inverse problems we will investigate novel approaches
for the following aspects specific to the above-mentioned problems in the life
sciences:



* Solution of inverse problems for PDEs in complex time-varying geometries

* Development of appropriate variational regularization models for dynamic
images, including noise and motion models

* Improved forward and inverse modelling of cellular and intracellular dynamics
leading to novel inverse problems for nonlinear partial differential equations

* Construction and implementation of efficient iterative solution methods for
the arising 4D inverse problems and their variational formulation All tasks
will be driven by concrete applications in biology and medicine and their
success will be evaluated in applications to real problems and data. This is
based on interdisciplinary work related to electrocardiology and developmental
biology. The overall development of methods will however be carried out in a
flexible and modular way, so that they become accessible for larger problem
classes.


External Partners

Westfälische Wilhelms-Universität (WWU) Münster

Last updated on 2019-15-02 at 22:00