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Efficient Total Variation Algorithm for Fetal Brain MRI Reconstruction

  • Sébastien Tourbier
  • Xavier Bresson
  • Patric Hagmann
  • Jean-Philippe Thiran
  • Reto Meuli
  • Meritxell Bach Cuadra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8674)

Abstract

Fetal MRI reconstruction aims at finding a high-resolution image given a small set of low-resolution images. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has considered several regularization terms s.a. Dirichlet/Laplacian energy [1], Total Variation (TV)-based energies [2,3] and more recently non-local means [4]. Although TV energies are quite attractive because of their ability in edge preservation, standard explicit steepest gradient techniques have been applied to optimize fetal-based TV energies. The main contribution of this work lies in the introduction of a well-posed TV algorithm from the point of view of convex optimization. Specifically, our proposed TV optimization algorithm for fetal reconstruction is optimal w.r.t. the asymptotic and iterative convergence speeds O(1/n2) and \(O(1/\sqrt{\varepsilon})\), while existing techniques are in O(1/n) and O(1/ε). We apply our algorithm to (1) clinical newborn data, considered as ground truth, and (2) clinical fetal acquisitions. Our algorithm compares favorably with the literature in terms of speed and accuracy.

Keywords

Fetal Brain Reconstruction Quality Normalize Root Mean Square Error Total Variation Energy SIAM Multiscale Modeling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sébastien Tourbier
    • 1
    • 2
  • Xavier Bresson
    • 1
    • 2
  • Patric Hagmann
    • 2
  • Jean-Philippe Thiran
    • 3
    • 2
  • Reto Meuli
    • 2
  • Meritxell Bach Cuadra
    • 1
    • 2
    • 3
  1. 1.Centre d’Imagerie BiomédicaleSwitzerland
  2. 2.Department of RadiologyLausanne University Hospital Center (CHUV) and University of Lausanne (UNIL)Switzerland
  3. 3.Signal Processing Laboratory (LTS5)Ecole Polytechnique Fédérale de Lausanne (EPFL)Switzerland

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