One‐Dimensional Fourier Imaging and k‐Space

Weili Lin1

1 University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
Publication Name:  Current Protocols in Magnetic Resonance Imaging
Unit Number:  Unit B4.2
DOI:  10.1002/0471142719.mib0402s00
Online Posting Date:  May, 2001
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Abstract

Magnetic resonance imaging offers the possibility to obtain spatially resolved anatomical information. This is accomplished by taking advantage of the Larmor relationship, which dictates that the frequency of the spins depends on the local magnetic field. This unit discusses the one dimensional Fourier imaging based on this relation. The one‐to‐one mapping of the signal from a given frequency to a given spatial location is explained. The image reconstruction based on well‐known Fourier transform reconstruction method is described in detail. The Fourier transform takes the MR signal as acquired in the time domain (usually referred to as the k‐space domain) and converts it to the frequency domain where 1‐D spatially resolved information can be obtained.

     
 
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Table of Contents

  • Overview
  • Technical Discussion
  • Key References
  • Figures
     
 
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Materials

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Figures

Videos

Literature Cited

Key References
   Haacke, E.M., Brown, R.W., Thompson, M.R., and Venkatesan, R. 1999. Magnetic Resonance Imaging: Physical Principles and Sequence Design. John Wiley & Sons, New York.
  This book covers the technical discussion here as well as other advanced materials in detail.
   Lauterbur, P.C. 1973. Image formation by induced local interactions. Examples employing magnetic resonance. Nature 243:190.
  This paper demonstrates the first imaging experiment using MRI.
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