Nonlocal operators, (p-)Laplace operator, Proximity, Basic functions, Fuzzy transform, Regularization problem

Regularization is a principle, concerning a wide range of science domains. Several methods, using this technique, have been proposed. However, there are some limitations to the functionals used in regularization. To remove these, the idea is to employ nonlocal operators on weighted graphs in regularization process. In images, pixels have a specific organization expressed by their spatial connectivity. Therefore, a typical structure used to represent images is a graph. The problem is to choose the correct one, because the topology of graphs can be arbitrary and each type of graph is proper to different type of problem. In this work, we focus on method based on nonlocal Laplace operator, which has become increasingly popular in image processing. Moreover, we introduce the representation of F-transform based Laplace operator.