A second-order model for image denoising

Maïtine Bergounioux (1) , Loïc Piffet (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We present a variational model for image denoising and/or texture identification. Noise and textures may be modelled as oscillating components of images. The model involves a L2- data fitting term and a Tychonov-like regularization term. We choose the BV2 norm instead of the classical BV norm. Here BV2 is the bounded hessian function space that we define and describe. The main improvement is that we do not observe staircasing effects any longer, during denoising process. Moreover, texture extraction can be performed with the same method. We give existence results and present a discretized problem. An algorithm close to one set by Chambolle is used: we prove convergence and present numerical tests.

Mots clés: Second order total variation; Image reconstruction; Denoising; texture; Variational method

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Loïc Piffet. A second-order model for image denoising. Set Valued Analysis, 2010, 18 (3-4), pp.277-306. ⟨10.1007/s11228-010-0156-6⟩. ⟨hal-00440872v2⟩