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Design of a logarithmic k ‐space spiral trajectory
Author(s) -
Cline Harvey E.,
Zong Xuli,
Gai Neville
Publication year - 2001
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.1309
Subject(s) - aliasing , trajectory , logarithmic spiral , spiral (railway) , k space , logarithm , image quality , traverse , curvature , mathematics , computer science , algorithm , mathematical analysis , physics , computer vision , image (mathematics) , geometry , fourier transform , undersampling , geodesy , astronomy , geography
Spiral acquisitions are used in fast cardiac imaging because they traverse k ‐space efficiently and minimize flow artifacts. A variable pitch logarithmic spiral trajectory is designed to critically sample the low‐frequency region in k ‐space and gradually undersample the high‐frequency region. An approximate analytical expression for the trajectory provides a fast means to calculate the gradient waveforms and the sampled data points. A numerical method is introduced based on the trajectory curvature and the rate of change in the gradient magnitude with time for the composite Archimedean‐logarithmic trajectory. The pulse sequence is implemented and images are acquired on phantoms and human hearts. The images show improved image resolution and some improvement in image quality as a result of increased extent in k ‐space and reduction in aliasing artifacts, respectively. Magn Reson Med 46:1130–1135, 2001. © 2001 Wiley‐Liss, Inc.