A Proximal Interior Point Algorithm with Applications to Image Processing

Emilie Chouzenoux (1, 2) , Marie-Caroline Corbineau (1, 2) , Jean-Christophe Pesquet (1, 2)

1 CVN - Centre de vision numérique
2 OPIS - OPtimisation Imagerie et Santé

In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nons-mooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying values of a logarithmic barrier parameter. This inner minimization is performed thanks to a finite number of subiterations of a variable metric forward-backward method employing a line search strategy. The convergence of this latter step as well as the convergence the global method itself are analyzed. The numerical efficiency of the proposed approach is demonstrated in two image processing applications.

Mots clés: Interior point methods; Armijo strategy; Proximity operator; proximity op- erator; constrained optimization; forward-backward algorithm; variable metric; line search; hyperspectral unmixing; geometry-texture decomposition

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

Emilie Chouzenoux, Marie-Caroline Corbineau, Jean-Christophe Pesquet. A Proximal Interior Point Algorithm with Applications to Image Processing. Journal of Mathematical Imaging and Vision, 2020, Special Issue on Memory of Mila Nikolova, 62 (6-7), p.919-940. ⟨10.1007/s10851-019-00916-w⟩. ⟨hal-02120005v2⟩