title: An image space approach to Cartesian based parallel MR imaging with total variation regularization.
abstract: The Cartesian parallel magnetic imaging problem is formulated variationally using a high-order penalty for coil sensitivities and a total variation like penalty for the reconstructed image. Then the optimality system is derived and numerically discretized. The objective function used is non-convex, but it possesses a bilinear structure that allows the ambiguity among solutions to be resolved technically by regularization and practically by normalizing a pre-estimated norm of the reconstructed image. Since the objective function 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 objective function is minimized with respect to one variable after the other using an inner generalized Newton iteration. Computational results for in vivo MR imaging data show that a significant improvement in reconstruction quality can be obtained by using the proposed regularization methods in relation to alternative approaches.
authors.affiliation: Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010 Graz, Austria. stephen.keeling@uni-graz.at
authors.forename: Stephen L
authors.initials: SL
authors.lastname: Keeling
authors.forename: Christian
authors.initials: C
authors.lastname: Clason
authors.forename: Michael
authors.initials: M
authors.lastname: Hintermüller
authors.forename: Florian
authors.initials: F
authors.lastname: Knoll
authors.forename: Antoine
authors.initials: A
authors.lastname: Laurain
authors.forename: Gregory
authors.initials: G
authors.lastname: von Winckel
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity