Parallel magnetic resonance imaging using the GRAPPA operator formalism.

Mark A Griswold; Martin Blaimer; Felix Breuer; Robin M Heidemann; Matthias Mueller; Peter M Jakob

doi:10.1002/mrm.20722

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Parallel magnetic resonance imaging using the GRAPPA operator formalism.

Mark A Griswold·Martin Blaimer·Felix Breuer·Robin M Heidemann·Matthias Mueller·Peter M Jakob

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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.

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Algorithms Brain Computing Methodologies Humans Image Enhancement Image Interpretation, Computer-Assisted Magnetic Resonance Imaging Phantoms, Imaging Reproducibility of Results Sensitivity and Specificity Journal Article Research Support, Non-U.S. Gov't

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Mark A Griswold, Martin Blaimer, Felix Breuer, Robin M Heidemann, Matthias Mueller, Peter M Jakob. 2005. Parallel magnetic resonance imaging using the GRAPPA operator formalism.. https://doi.org/10.1002/mrm.20722

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