A Variational Model for the Restoration of MR Images Corrupted by Blur and Rician Noise

  • Pascal Getreuer
  • Melissa Tong
  • Luminita A. Vese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6938)


In this paper, we propose a variational model to restore images degraded by blur and Rician noise. This model uses total variation regularization with a fidelity term involving the Rician probability distribution. For its numerical solution, we apply and compare the L 2 and Sobolev (H 1) gradient descents, and the iterative method called split Bregman (with a convexified fidelity term). Numerical results are shown on synthetic magnetic resonance imaging (MRI) data corrupted with Rician noise and Gaussian blur, both with known standard deviations.Theoretical analysis of the proposed model is briefly discussed.


Gradient Descent Gradient Descent Method Convex Approximation Gaussian Blur Total Variation Regularization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pascal Getreuer
    • 1
  • Melissa Tong
    • 2
  • Luminita A. Vese
    • 2
  1. 1.Centre de Mathématiques et de Leurs ApplicationsEcole Normale Supérieure de CachanFrance
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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