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Paper details
Number 1 - March 2021
Volume 31 - 2021
An unscented transformation approach to stochastic analysis of measurement uncertainty in magnet resonance imaging with applications in engineering
Andreas Rauh, Kristine John, Carolin Wüstenhagen, Martin Bruschewski, Sven Grundmann
Abstract
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.
Keywords
magnet resonance imaging, compressed sensing, stochastic uncertainty, unscented transformation