ON SOME PERTURBATIONS OF THE TOTAL VARIATION IMAGE INPAINTING METHOD. PART Ⅰ: REGULARITY THEORY

摘要

We investigate modifications of the total variation image inpainting model and discuss the existence as well as the smoothness of solutions to these new variational problems. We emphasize that our variant of a linear growth regularization is completely discussed in the Sobolev space W_1~1 without passing to a relaxed version in the space of functions with bounded variation. Our analysis mainly concentrates on the theoretical background of the problems under consideration. Nevertheless, first computational experiments indicate that our model is numerically comparable with the TV-model with the advantage of a clear underlying analysis presented in the following.