An unscented transformation approach to stochastic analysis of measurement uncertainty in magnet resonance imaging with applications in engineering
References
- Bouboulis, P. (2010). Wirtinger’s calculus in general Hilbert spaces, arXiv:1005.5170.
- Bruschewski, M., Freudenhammer, D., Buchenberg, W.B., Schiffer, H.-P. and Grundmann, S. (2016). Estimation of the measurement uncertainty in magnetic resonance velocimetry based on statistical models, Experiments in Fluids 57(5): 83.10.1007/s00348-016-2163-3
- Bruschewski, M., Kolkmann, H., John, K. and Grundmann, S. (2019). Phase-contrast single-point imaging with synchronized encoding: A more reliable technique for in vitro flow quantification, Magnetic Resonance in Medicine 81(5): 2937–2946.10.1002/mrm.2760430426563
- Datta, A., Kaur, A., Lauer, T. and Chabbouh, S. (2019). Exploiting multi-core and many-core parallelism for subspace clustering, International Journal of Applied Mathematics and Computer Science 29(1): 81–91, DOI: 10.2478/amcs-2019-0006.10.2478/amcs-2019-0006
- Elkins, C.J. and Alley, M.T. (2007). Magnetic resonance velocimetry: Applications of magnetic resonance imaging in the measurement of fluid motion, Experiments in Fluids 43(6): 823–858.10.1007/s00348-007-0383-2
- Gentleman, W.M. (1968). Matrix multiplication and fast Fourier transforms, Bell System Technical Journal 47(6): 1099–1103.10.1002/j.1538-7305.1968.tb00074.x
- Holland, D.J., Malioutov, D.M., Blake, A., Sederman, A.J. and Gladden, L.F. (2010). Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing, Journal of Magnetic Resonance 203(2): 236–246.10.1016/j.jmr.2010.01.00120138789
- Hörmander, L. (1990). An Introduction to Complex Analysis in Several Variables, 3rd Edn, North-Holland, Amsterdam.
- John, K., Jahangir, S., Gawandalkar, U., Hogendoorn, W., Poelma, C., Grundmann, S. and Bruschewski, M. (2020a). Magnetic resonance velocimetry in high-speed turbulent flows: Sources of measurement errors and a new approach for higher accuracy, Experiments in Fluids: Experimental Methods and Their Applications to Fluid Flow 61(2): 27.10.1007/s00348-019-2849-4
- John, K., Rauh, A., Bruschewski, M. and Grundmann, S. (2020b). Towards analyzing the influence of measurement errors in magnetic resonance imaging of fluid flows—Development of an interval-based iteration approach, Acta Cybernetica 24(3): 343–372.10.14232/actacyb.24.3.2020.5
- Julier, S., Uhlmann, J. and Durrant-Whyte, H. (2000). A new approach for the nonlinear transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control 45(3): 477–482.10.1109/9.847726
- Kostin, G.V., Saurin, V.V., Aschemann, H. and Rauh, A. (2014). Integrodifferential approaches to frequency analysis and control design for compressible fluid flow in a pipeline element, Mathematical and Computer Modelling of Dynamical Systems 20(5): 504–527.10.1080/13873954.2013.842595
- Măceş, D. and Stadtherr, M. (2013). Computing fuzzy trajectories for nonlinear dynamic systems, Computers & Chemical Engineering 52: 10–25.10.1016/j.compchemeng.2012.11.008
- Niebergall, A., Zhang, S., Kunay, E., Keydana, G., Job, M., Uecker, M. and Frahm, J. (2013). Real-time MRI of speaking at a resolution of 33 ms: Undersampled radial FLASH with nonlinear inverse reconstruction, Magnetic Resonance in Medicine 69(2): 477–485.10.1002/mrm.2427622498911
- Piegat, A. and Dobryakova, L. (2020). A decomposition approach to type 2 interval arithmetic, International Journal of Applied Mathematics and Computer Science 30(1): 185–201, DOI: 10.34768/amcs-2020-0015.
- Proakis, J.G. and Manolakis, D.G. (1996). Digital Signal Processing: Principles, Algorithms, and Applications, 3rd Edn, Prentice-Hall, Upper Saddle River.
- Rao, K.R. and Yip, P.C. (2000). The Transform and Data Compression Handbook, CRC Press, Boca Raton.10.1201/9781420037388
- Rauh, A., Dittrich, C., Senkel, L. and Aschemann, H. (2011). Sensitivity analysis for the design of robust nonlinear control strategies for energy-efficient pressure boosting systems in water supply, Proceedings of the 20th International Symposium on Industrial Electronics, ISIE 2011, Gdańsk, Poland, pp.1353–1358.
- Rauh, A., John, K., Bruschewski, M. and Grundmann, S. (2020). Comparison of two different interval techniques for analyzing the influence of measurement uncertainty in compressed sensing for magnet resonance imaging, Proceedings of the 18th European Control Conference, ECC 2020, St. Petersburg, Russia, pp. 1865–1870.
- Tamir, J., Ong, F., Cheng, J., Uecker, M. and Lustig, M. (2016). Generalized magnetic resonance image reconstruction using the Berkeley Advanced Reconstruction Toolbox, ISMRM Workshop on Data Sampling and Image Reconstruction, Sedona, USA, http://wwwuser.gwdg.de/~muecker1/sedona16-bart.pdf.
- Theilheimer, F. (1969). A matrix version of the fast Fourier transform, IEEE Transactions on Audio and Electroacoustics 17(2): 158–161.10.1109/TAU.1969.1162031
- Uhlmann, J. (2021). First-hand: The unscented transform, https://ethw.org/First-Hand:The_Unscented_Transform.
- Weinmann, A. (1991). Uncertain Models and Robust Control, Springer, Vienna.10.1007/978-3-7091-6711-3
- Zhao, F. (2014). Methods for MRI RF Pulse Design and Image Reconstruction, PhD thesis, University of Michigan, Ann Arbor.
- Zhao, F., Noll, D., Nielsen, J.-F. and Fessler, J. (2012). Separate magnitude and phase regularization via compressed sensing, IEEE Transactions on Medical Imaging 31(9): 1713–1723.10.1109/TMI.2012.2196707354528422552571
- Zhou, B., Yang, Y.-F. and Hu, B.-X. (2020). A second-order TV-based coupling model and an ADMM algorithm for MR image reconstruction, International Journal of Applied Mathematics and Computer Science 30(1): 113–122, DOI: 10.34768/amcs-2020-0009.
Language: English
Page range: 73 - 83
Submitted on: Jun 5, 2020
Accepted on: Dec 27, 2020
Published on: Apr 3, 2021
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
Related subjects:
© 2021 Andreas Rauh, Kristine John, Carolin Wüstenhagen, Martin Bruschewski, Sven Grundmann, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.