Journal of Mathematical Imaging and Vision

, Volume 38, Issue 3, pp 182–196 | Cite as

An Augmented Lagrangian Method for TV g +L 1-norm Minimization

  • Jonas Koko
  • Stéphanie Jehan-Besson


In this paper, the minimization of a weighted total variation regularization term (denoted TV g ) with L 1 norm as the data fidelity term is addressed using the Uzawa block relaxation method. The unconstrained minimization problem is transformed into a saddle-point problem by introducing a suitable auxiliary unknown. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional, we obtain a new numerical algorithm in which the main unknown is computed using Chambolle projection algorithm. The auxiliary unknown is computed explicitly. Numerical experiments show the availability of our algorithm for salt and pepper noise removal or shape retrieval and also its robustness against the choice of the penalty parameter. This last property is useful to attain the convergence in a reduced number of iterations leading to efficient numerical schemes. The specific role of the function g in TV g is also investigated and we highlight the fact that an appropriate choice leads to a significant improvement of the denoising results. Using this property, we propose a whole algorithm for salt and pepper noise removal (denoted UBR-EDGE) that is able to handle high noise levels at a low computational cost. Shape retrieval and geometric filtering are also investigated by taking into account the geometric properties of the model.


Total variation L1 norm Augmented Lagrangian Fenchel duality Uzawa methods Salt and pepper noise removal Shape retrieval Geometric filtering 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.LIMOSUniversité Blaise Pascal, CNRS UMR 6158AubiereFrance

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