An introduction to the Fourier transform: relationship to MRI.

Abstract

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. This article illustrates these basic Fourier principles and their relationship to MRI.