A total variation based approach to correcting surface coil magnetic resonance images
Keeling SL, Hintermueller M, Knoll F, Kraft D, Laurain A (2011)
Publication Type: Journal article
Publication year: 2011
Journal
Book Volume: 218
Pages Range: 219-232
Journal Issue: 2
DOI: 10.1016/j.amc.2011.03.002
Abstract
Magnetic resonance images which are corrupted by noise and by smooth modulations are corrected using a variational formulation incorporating a total variation like penalty for the image and a high order penalty for the modulation. The optimality system is derived and numerically discretized. The cost functional used is non-convex, but it possesses a bilinear structure which allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing the maximum value of the modulation. Since the cost is convex in each single argument, convex analysis is used to formulate the optimality condition for the image in terms of a primal-dual system. To solve the optimality system, a nonlinear Gauss-Seidel outer iteration is used in which the cost is minimized with respect to one variable after the other using an inner generalized Newton iteration. Favorable computational results are shown for artificial phantoms as well as for realistic magnetic resonance images. Reported computational times demonstrate the feasibility of the approach in practice. © 2011 Elsevier Inc. All rights reserved.
Authors with CRIS profile
Involved external institutions
Karl-Franzens-Universität Graz
Austria (AT)
Humboldt-Universität zu Berlin
Germany (DE)
Technische Universität Graz
Austria (AT)
Austria (AT)
Humboldt-Universität zu Berlin
Germany (DE)
Technische Universität Graz
Austria (AT)
How to cite
APA:
Keeling, S.L., Hintermueller, M., Knoll, F., Kraft, D., & Laurain, A. (2011). A total variation based approach to correcting surface coil magnetic resonance images. Applied Mathematics and Computation, 218(2), 219-232. https://doi.org/10.1016/j.amc.2011.03.002
MLA:
Keeling, Stephen L., et al. "A total variation based approach to correcting surface coil magnetic resonance images." Applied Mathematics and Computation 218.2 (2011): 219-232.
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