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 (Zielona Góra: Uniwersytet Zielonogórski)
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.
Keywords: magnet resonance imaging; compressed sensing; stochastic uncertainty; unscented transformation