An unscented transformation approach to stochastic analysis of measurement uncertainty in magnet resonance imaging with applications in engineering

Rauh, Andreas ; John, Kristine ; Wüstenhagen, Carolin ; Bruschewski, Martin ; Grundmann, Sven

International Journal of Applied Mathematics and Computer Science, Tome 31 (2021) no. 1, pp. 73-83.

Résumé

In the frame of stochastic filtering for nonlinear (discrete-time) dynamic systems, the unscented transformation plays a vital role in predicting state information from one time step to another and correcting a priori knowledge of uncertain state estimates by available measured data corrupted by random noise. In contrast to linearization-based techniques, such as the extended Kalman filter, the use of an unscented transformation not only allows an approximation of a nonlinear process or measurement model in terms of a first-order Taylor series expansion at a single operating point, but it also leads to an enhanced quantification of the first two moments of a stochastic probability distribution by a large signal-like sampling of the state space at the so-called sigma points which are chosen in a deterministic manner. In this paper, a novel application of the unscented transformation technique is presented for the stochastic analysis of measurement uncertainty in magnet resonance imaging (MRI). A representative benchmark scenario from the field of velocimetry for engineering applications which is based on measured data gathered at an MRI scanner concludes this contribution.

Détail

Keywords: magnet resonance imaging, compressed sensing, stochastic uncertainty, unscented transformation
Mots-clés : rezonans magnetyczny, próbkowanie oszczędne, niepewność stochastyczna

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