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: Variable metric; Line search; Armijo strategy; Hyperspectral unmixing; Geometry-texture decomposition; Interior point methods; Forward-backward algorithm; Constrained optimization; Proximity operator

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, In press. ⟨hal-02120005v1⟩