Michael Hintermüller, Tobias Schäffter
Staff: Gouzhi Dong (HU & WIAS)
Associate: Kostas Papafitsoros (WIAS)
01.01.2019 – 31.12.2021
Model-based imaging requires knowledge on some physical models. This is often challenge in real applications, as the physical models might be not directly available, but hidden in different kinds of data, either experimentally or numerically. This project aims to develop the concept of model-based imaging methods. The idea is integrating physical models, either dictionary based or learning-informed, into the image reconstruction process. These new mathematical objects then need to be analytically and numerically investigated, including also robust numerical solvers.
Exemplary case study focuses on magnetic resonance imaging. An integrated physics-based models are proposed for quantitatively estimating the tissue parameters, for instance, the T1/T2 relaxation time, the proton spin density. Approaches of using learning-informed physics or dictionary-based physics are under investigation.
Imaging techniques using bilevel optimization schemes and PDE tools have been studied in different context.
G. Dong, M. Hintermüller, K. Papafitsoros, Quantitative magnetic resonance imaging: From fingerprinting to integrated physics-based models, SIAM Journal on Imaging Sciences, 2 (2019), pp. 927–971, DOI 10.1137/18M1222211 .
M. Hintermüller, K. Papafitsoros, Chapter 11: Generating structured nonsmooth priors and associated primal-dual methods, in: Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, R. Kimmel, X.-Ch. Tai, eds., 20 of Handbook of Numerical Analysis, Elsevier, 2019, pp. 437–502, (Chapter Published), DOI 10.1016/bs.hna.2019.08.001.
G. Dong, M. Hintermüller, Y. Zhang, A class of geometric second order quasi-linear hyperbolic PDEs and their application in imaging science. WIAS Preprint No. 2591, (2019).
M. Hintermüller, K. Papafitsoros, C. N. Rautenberg, H. Sun, Dualization and automatic distributed parameter selection of total generalized variation via bilevel optimization, WIAS Preprint No. 2689, (2020).
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