Some applications of $l^\infty$-constraints in image processing

Pierre Weiss (1) , Gilles Aubert (2) , Laure Blanc-Féraud (1)

1 ARIANA - Inverse problems in earth monitoring
2 JAD - Laboratoire Jean Alexandre Dieudonné

Our goal in this paper is to give algorithms for minimizing generic regularizing functionals under a $l^\infty$-constraint. We show that many classical models using total variation can be stated under this formalism. Among others are the Rudin-Oscher-Fatemi model, the BV-l1 model, BV-$l^\infty$ model and Meyer's cartoon +texture decomposition model. Then we describe a general convergence algorithm to solve such problems. This algorithm is the projected subgradient descent. We finally give numerical results that show the qualities and limits of our model, and we tackle the question of the use of the total variation to treat bounded noises such as quantization noise.

Mots clés: compression noise; quantization noise; $l^\infty$-norm; total variation minimization; bounded noises; duality; projected subgradient descent

Domaines: Traitement des images [eess.IV]

Pierre Weiss, Gilles Aubert, Laure Blanc-Féraud. Some applications of $l^\infty$-constraints in image processing. [Research Report] RR-6115, INRIA. 2006, pp.33. ⟨inria-00114051v2⟩