An introduction to the Fourier transform: relationship to MRI.
OBJECTIVE
The Fourier transform, a fundamental mathematic tool widely used in signal analysis, is ubiquitous in radiology and integral to modern MR image formation. Understanding MRI techniques requires a basic understanding of what the Fourier transform accomplishes. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform.


CONCLUSIONS
This article illustrates these basic Fourier principles and their relationship to MRI.
Gallagher
Thomas A
TA
Department of Radiology, Loyola University Medical Center, 2160 S First Ave., Maywood, IL 60153, USA. tgalla1@lumc.edu
Nemeth
Alexander J
AJ
Hacein-Bey
Lotfi
L
D016477:Artifacts; D005583:Fourier Analysis; D006801:Humans; D008279:Magnetic Resonance Imaging