Proximal method for geometry and texture image decomposition

Luis M. Briceno-Arias (1) , Patrick Louis Combettes (1) , Jean-Christophe Pesquet (2) , Nelly Pustelnik (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We propose a variational method for decomposing an image into a geometry and a texture component. Our model involves the sum of two functions promoting separately properties of each component, and of a coupling function modeling the interaction between the components. None of these functions is required to be differentiable, which significantly broadens the range of decompositions achievable through variational approaches. The convergence of the proposed proximal algorithm is guaranteed under suitable assumptions. Numerical examples are provided that show an application of the algorithm to image decomposition and restoration in the presence of Poisson noise.

Mots clés: Convex optimization; denoising; image decomposition; image restoration; proximity operator

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Luis M. Briceno-Arias, Patrick Louis Combettes, Jean-Christophe Pesquet, Nelly Pustelnik. Proximal method for geometry and texture image decomposition. IEEE International Conference on Image Processing (ICIP), Sep 2010, Hong-Kong, Hong Kong SAR China. pp.x+4. ⟨hal-00826120⟩