Tikhonov regularization and constrained quadratic programming for magnetic coil design problems
By: Bartłomiej Garda and Zbigniew Galias
References
- Bro, R. and Jong, S.D. (1997). A fast non-negativityconstrained least squares algorithm,(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,(3): 369–376.
- Garda, B. (2012). Linear algebra approach and the quasi-Newton algorithm for the optimal coil design problem,(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,, pp. 508–511.
- Garda, B. and Galias, Z. (2012). Non-negative least squares and the Tikhonov regularization methods for coil design problems,.
- Hansen, P. (1998)., IMM-REP, Institut for Matematisk Modellering, Danmarks Tekniske Universitet, Kongens Lyngby.
- Jin, J. (1999)., Biomedical Engineering Series, CRC Press, Boca Raton, FL.
- Lawson, C. and Hanson, R. (1987)., 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,(2): 476–483.
- Prasath, V.B.S. (2011). A well-posed multiscale regularization scheme for digital image denoising,(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,(3): 135–156.
- Szynkiewicz, W. and Błaszczyk, J. (2011). Optimization-based approach to path planning for closed chain robot systems,(4): 659–670, DOI: 10.2478/v10006-011- 0052-8.
- Tikhonov, A. and Arsenin, V. (1977)., Scripta Series in Mathematics, John Wiley&Sons, Washington, DC.
- Turner, R. (1986). A target field approach to optimal coil design,(8): 147–151.
- Voglis, C. and Lagaris, I. (2004). BOXCQP: An algorithm for bound constrained convex quadratic problems,.
- Xu, H., Conolly, S., Scott, G. and Macovski, A. (1999). Fundamental scaling relations for homogeneous magnets,, 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,(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 issues per year
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© 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.