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Natural k ‐plane coordinate reconstruction method for magnetic resonance imaging: Mathematical foundations
Author(s) -
Sarty Gordon E.
Publication year - 1997
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(1997)8:6<519::aid-ima4>3.0.co;2-d
Subject(s) - magnetic resonance imaging , plane (geometry) , coordinate system , computer science , nuclear magnetic resonance , physics , geometry , mathematics , artificial intelligence , radiology , medicine
The mathematical basis and motivation for a new, noninterpolative, direct method for reconstructing magnetic resonance imaging (MRI) data is presented. The reconstruction method is called the natural k ‐plane coordinate reconstruction method (NKPCRM) and can be used for reconstructing MRI data collected in the presence of continuously varying gradient magnetic fields. A continuous, theoretically useful NKPCRM is presented along with a practical discrete NKPCRM both for single‐ and multiple‐shot data acquisitions. The continuous method gives rise to continuous operators on function spaces that can be characterized as integrable curve band‐pass operators. The discrete reconstruction method reduces to a Fourier summation weighted by the Jacobian of a “naturally” chosen coordinate system. In the case of a Cartesian coordinate system, the new method reduces to the discrete Fourier transform normally used for MRI reconstruction. The NKPCRM is rigorously analyzed from a mathematical point of view, and specific implementations such as Lissajous, spiral, and rose scans are discussed. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 519–528, 1997