Mathematical and numerical analysis of a variational second order image decomposition model

Maïtine Bergounioux (1)

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

We deal with a second order image decomposition model to perform denoising and texture extraction that was previously presented in \cite{BP2}. We look for the decomposition f= u+v + w where u is a first order term, v a second order term and w the remainder term (0 order). For highly textured images the model gives a two-scale texture decomposition: u can be viewed as a ''macro-texture'' (larger scale) which oscillations are not too large and w is the ''micro-texture'' (very oscillating) that contains the noise. Here, we perform mathematical analysis of the model and give qualitative properties of solutions using the dual problem and inf-convolution formulation. Then we perform numerical experiments, discuss the behavior of the model and investigate the lack of uniqueness.

Mots clés: Second order total variation; image decomposition; variational method; inf-convolution

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

Maïtine Bergounioux. Mathematical and numerical analysis of a variational second order image decomposition model. 2014. ⟨hal-01002958v1⟩