Continuous Primal-Dual Methods for Image Processing

Michael Goldman (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this article we study a continuous Primal-Dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow-Hurwicz method which leads to a better description of the system of PDEs obtained. We show existence and uniqueness of solutions and get a convergence result for the denoising problem. Our analysis also yields new a posteriori estimates.

Mots clés: Primal-Dual Methods; Total Variation regularization; a posteriori estimates

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Michael Goldman. Continuous Primal-Dual Methods for Image Processing. SIAM Journal on Imaging Sciences, 2011, 4 (1), pp.366-385. ⟨10.1137/100789178⟩. ⟨hal-00464652v2⟩