Application of the fractional fourier transform to image reconstruction in MRI

Vicente Parot, Carlos Sing-Long, Carlos Lizama, Cristian Tejos, Sergio Uribe, Pablo Irarrazaval

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)


The classic paradigm for MRI requires a homogeneous B0 field in combination with linear encoding gradients. Distortions are produced when the B0 is not homogeneous, and several post-processing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B0 fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding.

Original languageEnglish
Pages (from-to)17-29
Number of pages13
JournalMagnetic Resonance in Medicine
Issue number1
Publication statusPublished - Jul 2012
Externally publishedYes


  • Field inhomogeneities
  • Fractional fourier transform
  • Image reconstruction
  • Magnetic resonance imaging
  • Nonlinear encoding
  • Off-resonance correction

Cite this