Analysis of a Variational Framework for Exemplar Based Image Inpainting

Presented at the 2012 SIAM Conference on Imaging Science, Mini-Symposium: “Recent Advances in Patch-based Image Processing”. May 20-22 2012, Philadelphia, PA, USA.

We discuss a variational framework for exemplar based image inpainting, in which both the reconstructed image u and the non-local weights w are treated as variables and updated using the variational formulation. This approach permits to draw relations with some existing inpainting schemes, in addition to leading to novel ones. We carry out an analysis of two of these schemes providing existence of the solution, regularity of the minima and convergence of the alternating scheme for the variables (u,w).