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Noise Modelling in Parallel Magnetic Resonance Imaging: A Variational Approach

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Image Analysis and Recognition (ICIAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8814))

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Abstract

We proposed a new variational model for parallel Magnetic Resonance Imaging (MRI) processing including denoising, deblurring and super-resolution. In the context of Maximum A Posteriori (MAP) estimation it takes into account the non-central \(\chi \) (nc-\(\chi \)) distribution of the noise in parallel magnitude magnetic resonance (MR) images. This leads to the resolution of an energy minimization problem. In this Bayesian modelling framework the Total Generalized Variation (TGV) is proposed as the regularization term. A primal-dual algorithm is then implemented to solve numerically the presented model. The effectiveness of our approach is shown through a successful comparison of its performance to previous TGV methods for MRI denoising based on Gaussian noise.

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Authors and Affiliations

  1. Applied Mathematics Department, Universidad Rey Juan Carlos, 28933, Móstoles, Madrid, Spain

    Adrián Martín & Emanuele Schiavi

  2. Magnetic Resonance Imaging Group, RLE-EECS, Massachusetts Institute of Technology, Cambridge, MA, USA

    Adrián Martín

Authors
  1. Adrián Martín
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  2. Emanuele Schiavi
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Corresponding author

Correspondence to Adrián Martín .

Editor information

Editors and Affiliations

  1. Faculty of Engineering, University of Porto, Porto, Portugal

    Aurélio Campilho

  2. Dept. of Electrical and Computer Eng., University of Waterloo, Waterloo, Ontario, Canada

    Mohamed Kamel

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Martín, A., Schiavi, E. (2014). Noise Modelling in Parallel Magnetic Resonance Imaging: A Variational Approach. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2014. Lecture Notes in Computer Science(), vol 8814. Springer, Cham. https://doi.org/10.1007/978-3-319-11758-4_14

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  • DOI: https://doi.org/10.1007/978-3-319-11758-4_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11757-7

  • Online ISBN: 978-3-319-11758-4

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