title: Parallel magnetic resonance imaging using the GRAPPA operator formalism.
abstract: In this article it is shown that GRAPPA reconstruction can be reformulated as a matrix operator, similar to ladder or propagator operators used in quantum mechanics, that shifts data in k-space. Using this formalism, it is shown that there exists an infinitesimal GRAPPA operator that shifts data in k-space by arbitrarily small amounts. Other desired k-space shifts can then be accomplished through repeated applications of this infinitesimal GRAPPA operator. Implications of these ideas are described.
authors.affiliation: University of Würzburg, Department of Physics, EP5, Würzburg, Germany. mark@physik.uni-wuerzburg.de
authors.forename: Mark A
authors.initials: MA
authors.lastname: Griswold
authors.forename: Martin
authors.initials: M
authors.lastname: Blaimer
authors.forename: Felix
authors.initials: F
authors.lastname: Breuer
authors.forename: Robin M
authors.initials: RM
authors.lastname: Heidemann
authors.forename: Matthias
authors.initials: M
authors.lastname: Mueller
authors.forename: Peter M
authors.initials: PM
authors.lastname: Jakob
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D003205:Computing Methodologies; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity