Tikhonov regularization and constrained quadratic programming for magnetic coil design problems
By:
References
- Bro, R. and Jong, S.D. (1997). A fast non-negativityconstrained least squares algorithm, Journal of Chemometrics11(5): 393–401.
- Fisher, B.J., Dillon, N., Carpenter, T.A. and Hall, L.D. (1997). Design of a biplanar gradient coil using a genetic algorithm, Magnetic Resonance Imaging15(3): 369–376.
- Garda, B. (2012). Linear algebra approach and the quasi-Newton algorithm for the optimal coil design problem, Przegla˛d Elektrotechniczny (7a): 261–264.
- Garda, B. and Galias, Z. (2010). Comparison of the linear algebra approach and the evolutionary computing for magnetic field shaping in linear coils, Nonlinear Theory and Its Applications, NOLTA 2010, Cracow, Poland, pp. 508–511.
- Garda, B. and Galias, Z. (2012). Non-negative least squares and the Tikhonov regularization methods for coil design problems, Proceedings of the International Conference on Signals and Electronic Systems, ICSES 2012, Wrocław, Poland.
- Hansen, P. (1998). Regularization Tools: A Matlab Package for Analysis and Solution of Discrete Ill-posed Problems. Version 3.0 for Matlab 5.2, IMM-REP, Institut for Matematisk Modellering, Danmarks Tekniske Universitet, Kongens Lyngby.
- Jin, J. (1999). Electromagnetic Analysis and Design in Magnetic Resonance Imaging, Biomedical Engineering Series, CRC Press, Boca Raton, FL.
- Lawson, C. and Hanson, R. (1987). Solving Least Squares Problems, Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, PA.
- Macovski, A., Xu, H., Conolly, S. and Scott, G. (2000). Homogeneous magnet design using linear programing, IEEE Transactions on Magnetics36(2): 476–483.
- Prasath, V.B.S. (2011). A well-posed multiscale regularization scheme for digital image denoising, International Journal of AppliedMathematics and Computer Science21(4): 769– 777, DOI: 10.2478/v10006-011-0061-7.
- Sikora, R., Kraso´n, P. and Gramz, M. (1980). Magnetic field synthesis at the plane perpendicular to the axis of solenoid, Archiv fur elektrotechnik62(3): 135–156.
- Szynkiewicz, W. and Błaszczyk, J. (2011). Optimization-based approach to path planning for closed chain robot systems, International Journal of Applied Mathematics and Computer Science21(4): 659–670, DOI: 10.2478/v10006-011- 0052-8.
- Tikhonov, A. and Arsenin, V. (1977). Solutions of Ill-posed Problems, Scripta Series in Mathematics, John Wiley&Sons, Washington, DC.
- Turner, R. (1986). A target field approach to optimal coil design, Journal of Physics D: Applied Physics19(8): 147–151.
- Voglis, C. and Lagaris, I. (2004). BOXCQP: An algorithm for bound constrained convex quadratic problems, Proceedings of the 1st International Conference: From Scientific Computing to Computational Engineering, IC-SCCE, Athens, Greece.
- Xu, H., Conolly, S., Scott, G. and Macovski, A. (1999). Fundamental scaling relations for homogeneous magnets, ISMRM 7th Scientific Meeting, Philadelphia, PA, USA, p. 475.
- Zhu, M., Xia, L., Liu, F., Zhu, J., L. Kang and Crozier, S. (2012). Finite difference method for the design of gradient coils in MRI—Initial framework, IEEE Transactions on Biomedical Engineering59(9): 2412–2421.
Language: English
Page range: 249 - 257
Submitted on: Jan 20, 2013
Published on: Jun 26, 2014
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Related subjects:
© 2014 Bartłomiej Garda, Zbigniew Galias, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.