Journal of Scientific Computing

, Volume 37, Issue 2, pp 103–138 | Cite as

Non-smooth SOR for L 1-Fitting: Convergence Study and Discussion of Related Issues

  • R. Glowinski
  • T. KärkkäinenEmail author
  • T. Valkonen
  • A. Ivannikov


In this article, the denoising of smooth (H 1-regular) images is considered. To reach this objective, we introduce a simple and highly efficient over-relaxation technique for solving the convex, non-smooth optimization problems resulting from the denoising formulation. We describe the algorithm, discuss its convergence and present the results of numerical experiments, which validate the methods under consideration with respect to both efficiency and denoising capability. Several issues concerning the convergence of an Uzawa algorithm for the solution of the same problem are also discussed.


Denoising Non-smooth objective function Convex analysis Over-relaxation 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • R. Glowinski
    • 1
  • T. Kärkkäinen
    • 2
    Email author
  • T. Valkonen
    • 2
  • A. Ivannikov
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Department of Mathematical Information TechnologyUniversify of JyväskyläUniversity of JyväskyläFinland

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