Journal of Scientific Computing

, Volume 19, Issue 1, pp 95–122

TV Based Image Restoration with Local Constraints


  • M. Bertalmio
    • Department of TecnologiaUniversitat Pompeu Fabra
  • V. Caselles
    • Department of TecnologiaUniversitat Pompeu Fabra
  • B. Rougé
    • CNES
  • A. Solé
    • Department of TecnologiaUniversitat Pompeu Fabra

DOI: 10.1023/A:1025391506181

Cite this article as:
Bertalmio, M., Caselles, V., Rougé, B. et al. Journal of Scientific Computing (2003) 19: 95. doi:10.1023/A:1025391506181


The problem of recovering an image that has been blurred and corrupted with additive noise is ill-posed. Among the methods that have been proposed to solve this problem, one of the most successful ones is that of constrained Total Variation (TV) image restoration, proposed by L. Rudin, S. Osher, and E. Fatemi. In its original formulation, to ensure the satisfaction of constraints, TV restoration requires the estimation of a global parameter λ (a Lagrange multiplier). We observe that if λ is global, the constraints of the method are also satisfied globally, but not locally. The effect is that the restoration is better achieved in some regions of the image than in others. To avoid this, we propose a variant of the TV restoration model including, instead of a single constraint λ, a set of constraints λi, each one corresponding to a region Oi of the image. We discuss the existence and uniqueness of solutions of the proposed model and display some numerical experiments.

image restorationTotal Variationvariational methodssatellite images
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© Plenum Publishing Corporation 2003