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Regularization techniques on least squares non-uniform fast Fourier transform

Authors

  • Fabio Gibiino,

    Corresponding author
    • Department of Energy and System Engineering, University of Pisa, Pisa, Italy
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  • Vincenzo Positano,

    1. Fond. G. Monasterio, CNR Regione Toscana, Pisa, Italy
    2. Institute of Clinical Physiology, National Research Council, Pisa, Italy
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  • Luigi Landini,

    1. Fond. G. Monasterio, CNR Regione Toscana, Pisa, Italy
    2. Institute of Clinical Physiology, National Research Council, Pisa, Italy
    3. Department of Information Engineering EIT, University of Pisa, Pisa, Italy
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  • Maria Filomena Santarelli

    1. Fond. G. Monasterio, CNR Regione Toscana, Pisa, Italy
    2. Institute of Clinical Physiology, National Research Council, Pisa, Italy
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Correspondence to: Fabio Gibiino, Dipartimento di Ingegneria dell'Energia e dei Sistemi - University of Pisa. Largo Lucio Lazzarino 1 - 56122 Pisa - Italy.

E-mail: f.gibiino@gmail.com

SUMMARY

Non-Cartesian acquisition strategies are widely used in MRI to dramatically reduce the acquisition time while at the same time preserving the image quality. Among non-Cartesian reconstruction methods, the least squares non-uniform fast Fourier transform (LS_NUFFT) is a gridding method based on a local data interpolation kernel that minimizes the worst-case approximation error. The interpolator is chosen using a pseudoinverse matrix. As the size of the interpolation kernel increases, the inversion problem may become ill-conditioned. Regularization methods can be adopted to solve this issue. In this study, we compared three regularization methods applied to LS_NUFFT. We used truncated singular value decomposition (TSVD), Tikhonov regularization and L1-regularization. Reconstruction performance was evaluated using the direct summation method as reference on both simulated and experimental data. We also evaluated the processing time required to calculate the interpolator. First, we defined the value of the interpolator size after which regularization is needed. Above this value, TSVD obtained the best reconstruction. However, for large interpolator size, the processing time becomes an important constraint, so an appropriate compromise between processing time and reconstruction quality should be adopted. Copyright © 2013 John Wiley & Sons, Ltd.

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