Final Report Summary - LIFEINVERSE (Variational Methods for Dynamic Inverse Problems in the Life Sciences)
This project was developing novel techniques for solving inverse problems in life sciences, in particular related to dynamic imaging. Modern biomedical imaging techniques such as fluorescence microscopy, dynamic MR and CT, PET, or electromagnetic imaging were investigated with respect to two aspects:
1. The improved reconstruction of images and videos from low quality data.
2. The quantification of imaging data via mathematical models based on (systems of) partial differential equations.
Both aspects were tackled with in the framework of inverse problems, using advanced mathematical models and modern variational regularization methods for their solution.
The project provided novel techniques for the solution of such inverse problems in complex time-varying domains (again obtained from imaging data) by devising and analyzing diffuse domain descriptions that can be efficiently derived from the data. Based on those improved models for several biomedical problems such as the imaging of the epicardial potential on the beating heart surfaces or the quantification of intracellular motion inside moving cells could be treated and led to novel insights. These techniques were combined with novel approaches for the variational regularization in the reconstruction of dynamic images, a particular highlight being methods that efficiently reconstruct image sequences with nonrigid underlying motion. In this way not only the motion is corrected, but the coherence between consecutive time frames is used to achieve superresolution (e.g. in microscopy) or keep resolution at decreasing amount of data (e.g. in CT in order to minimize radiation exposure).
For all the models efficient computational methods have been constructed in a unified way, leading to a high-end software based on a unified description of imaging data as discrete functions on graphs and an easily useable software package for rapid prototyping in MATLAB.
1. The improved reconstruction of images and videos from low quality data.
2. The quantification of imaging data via mathematical models based on (systems of) partial differential equations.
Both aspects were tackled with in the framework of inverse problems, using advanced mathematical models and modern variational regularization methods for their solution.
The project provided novel techniques for the solution of such inverse problems in complex time-varying domains (again obtained from imaging data) by devising and analyzing diffuse domain descriptions that can be efficiently derived from the data. Based on those improved models for several biomedical problems such as the imaging of the epicardial potential on the beating heart surfaces or the quantification of intracellular motion inside moving cells could be treated and led to novel insights. These techniques were combined with novel approaches for the variational regularization in the reconstruction of dynamic images, a particular highlight being methods that efficiently reconstruct image sequences with nonrigid underlying motion. In this way not only the motion is corrected, but the coherence between consecutive time frames is used to achieve superresolution (e.g. in microscopy) or keep resolution at decreasing amount of data (e.g. in CT in order to minimize radiation exposure).
For all the models efficient computational methods have been constructed in a unified way, leading to a high-end software based on a unified description of imaging data as discrete functions on graphs and an easily useable software package for rapid prototyping in MATLAB.