An introduction to the Fourier transform: Relationship to MRI

Thomas A. Gallagher, Alexander J. Nemeth, Lotfi Hacein-Bey

Research output: Contribution to journalReview articlepeer-review

51 Scopus citations


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

Original languageEnglish (US)
Pages (from-to)1396-1405
Number of pages10
JournalAmerican Journal of Roentgenology
Issue number5
StatePublished - May 2008


  • Fourier transform
  • Gibbs artifact
  • K-space

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


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