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1 International Journal of Applied Mathematics and Computer Science

1 2021

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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

2021

Vol. 31, no. 1

73--83

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.