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    A physically oriented method for quantitative magnetic resonance imaging
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Dong, Guozhi; Hintermüller, Michael; Papafitsoros, Kostas
    Quantitative magnetic resonance imaging (qMRI) denotes the task of estimating the values of magnetic and tissue parameters, e.g., relaxation times T1, T2, proton density p and others. Recently in [Ma et al., Nature, 2013], an approach named Magnetic Resonance Fingerprinting (MRF) was introduced, being capable of simultaneously recovering these parameters by using a two step procedure: (i) a series of magnetization maps are created and then (ii) these are matched to parameters with the help of a pre-computed dictionary (Bloch manifold). In this paper, we initially put MRF and its variants in the perspective of optimization and inverse problems, providing some mathematical insights into these methods. Motivated by the fact that the Bloch manifold is non-convex, and the accuracy of the MRF type algorithms is limited by the discretization size of the dictionary, we propose here a novel physically oriented method for qMRI. In contrast to the conventional two step models, our model is dictionary-free and it is described by a single nonlinear equation, governed by an operator for which we prove differentiability and other properties. This non-linear equation is efficiently solved via robust Newton type methods. The effectiveness of our method for noisy and undersampled data is shown both analytically and via numerical examples where also improvement over MRF and its variants is observed.
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    Phase transformation modeling and parameter identification from dilatometric investigations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Suwanpinij, Piyada; Togobytska, Nataliya; Keul, Christoph; Weiss, Wolf; Prahl, Ulrich; Hömberg, Dietmar; Bleck, Wolfgang
    The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations.