Regularized non-local Total Variation and application in image restoration

Zhi Li (1) , François Malgouyres (2) , Tieyong Zeng (1)

1 HKBU - Hong Kong Baptist University
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In the usual non-local variational models, such as the non-local total variations (NLTV), the image is regularized by minimizing an energy term that penalizes gray-levels discrepancy between some specified pairs of pixels, a weight value is computed between these two pixels to penalize their dissimilarity. In this paper, we impose some regularity to those weight values. More precisely, we minimize a function involving a regularization term, analogous to an $H^1$ term, on weights. Doing so, the finite differences defining the image regularity depend on their environment. When the weights are difficult to define, they can be restored by the proposed stable regularization scheme. We provide all the details necessary for the implementation of a PALM algorithm with proved convergence. We illustrate the ability of the model to restore relevant unknown edges from the neighboring edges on an image inpainting problem. We also argue on inpainting, zooming and denoising problems that the model better recovers thin structures.

Mots clés: image restoration; total variation; non-local regularization; proximal alternating linearized minimization; nonconvex minimization

Domaines: Optimisation et contrôle [math.OC]; Traitement des images [eess.IV]

Zhi Li, François Malgouyres, Tieyong Zeng. Regularized non-local Total Variation and application in image restoration. Journal of Mathematical Imaging and Vision, 2017, 59 (2), pp.296-317. ⟨10.1007/s10851-017-0732-6⟩. ⟨hal-01342111v3⟩