F-transform-Based Optimization for Image Restoration (Inpainting)

In image processing, the inpainting (image restoration) problem is often considered with respect to the interpolation. We involve into the solution of this problem the F-transform-based nonlocal operators that define a new type of functionals, extending the ability of classical PDE-based algorithms in handling textures and repetitive structures. We showed that in the particular space with a fuzzy partition, the nonlocal Laplacian and partial derivatives can be represented by the F0- and F1-transforms. For the inpainting problem specified by relatively large damaged areas, we propose a new total variation model with the F-transform-based nonlocal operators. We show that the proposed model together with the corresponding algorithm increase the quality of a (usually considered) patch-based searching algorithm.