Singular Feature Extraction and Artefact Reduction in Dynamic Imaging

• Applicant: Professorin Dr. Bernadette Hahn-Rigaud
• Subject Area: Mathematics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 329129802

Imaging modalities are concerned with the non-invasive recovery of some characteristic functions of an object under investigation, and hence represent a well-known application of the theory of inverse problems. For most of them, the sought-for functions are assumed to be independent of time. However, this assumption is violated in many medical and industrial applications, e.g. due to patient and organ motion or while imaging engines at working stage. In this case, the standard reconstruction techniques lead to motion artefacts in the computed images which can significantly impede a reliable diagnostics. To compensate for the motion implies to incorporate the time-dependency of the investigated object in the inverse problem associated to the static case. Adding the time dimension to the searched-for quantity does not only lead to an underdetermined problem, it also alters the nature of the static problem such as the degree of ill-posedness, the spatial resolution or lead to limited data issues. This project intends to address these points by the development of a regularization theory for dynamic imaging.For this purpose, the project is divided in two parts: First, we propose to study and solve the dynamic problem for known motion. In particular, we shall analyse the effect of the motion on the ill-posedness, deal with limited data problems arising from local deformations, develop efficient and regularized inversion schemes and then study the sensitivity of the methods to the parameters of the motion model. The second part is devoted to estimate the motion directly from the motion-corrupted data and thus to extend the theory from the first step to unknown deformations. The ignorance of both motion and searched-for-quantity brings the dynamic inverse problem to be highly underdetermined. At this end, we propose to exploit the sparsity of well chosen features, for instance wavelets or contours for piecewise constant functions, which will inherently reduce the underdeterminancy of the considered problem. Altogether, the project will result in a joint motion estimation and image reconstruction procedure which reduces the motion artefacts in the image and hence helps for the diagnosis.The project is dedicated to significantly improve the quality of reconstruction in tomographic applications affected by object related motion and to enable the non-invasive visualization of faster time-evolving processes than at present, for instance in fluid flow studies.

• DFG Programme: Research Grants