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Application of the fractional Fourier transform to image reconstruction in MRI
Author(s) -
Parot Vicente,
SingLong Carlos,
Lizama Carlos,
Tejos Cristian,
Uribe Sergio,
Irarrazaval Pablo
Publication year - 2012
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.23190
Subject(s) - fourier transform , fractional fourier transform , nonlinear system , homogeneity (statistics) , quadratic equation , computer science , algorithm , field (mathematics) , fourier analysis , mathematics , mathematical analysis , physics , geometry , quantum mechanics , machine learning , pure mathematics
Abstract The classic paradigm for MRI requires a homogeneous B 0 field in combination with linear encoding gradients. Distortions are produced when the B 0 is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short‐bore magnets and higher B 0 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. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.