Application of the fractional Fourier transform to image reconstruction in MRI

Authors

  • Vicente Parot,

    1. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
    2. Department of Electrical Engineering and Department of Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile
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  • Carlos Sing-Long,

    1. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
    2. Department of Electrical Engineering and Department of Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile
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  • Carlos Lizama,

    1. Department of Electrical Engineering and Department of Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile
    2. Department of Mathematics and Computer Science, Universidad de Santiago de Chile, Santiago, Chile
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  • Cristian Tejos,

    1. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
    2. Department of Electrical Engineering and Department of Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile
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  • Sergio Uribe,

    1. Department of Electrical Engineering and Department of Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile
    2. Department of Radiology, Pontificia Universidad Católica de Chile, Santiago, Chile
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  • Pablo Irarrazaval

    Corresponding author
    1. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
    2. Department of Electrical Engineering and Department of Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile
    • Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Av. Vicuna Mackenna 4860, Macul 7820436, Santiago, Chile
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Abstract

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 postprocessing 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. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.

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