Parallel magnetic resonance imaging using the GRAPPA operator formalism.
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.
Griswold
Mark A
MA
University of Würzburg, Department of Physics, EP5, Würzburg, Germany. mark@physik.uni-wuerzburg.de
Blaimer
Martin
M
Breuer
Felix
F
Heidemann
Robin M
RM
Mueller
Matthias
M
Jakob
Peter M
PM
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