Scattered data interpolation is very important problem and solution of this task is required by great amount of fields. In the scope of this project we are focusing on interpolation of 2D images from scattered set of points. Different classes of methods for solution of this task are available. Among these methods best performance is presented by so-called radial basis function (RBF) interpolation. We propose new interpolation solution based on second order partial differential equations which can outperform even RBF approaches. Main attention is devoted to particular modification of anisotropic diffusion process, namely edge enhancing diffusion (EED). To enlarge efficiency and flexibility of the method some theoretical and practical issues of finite element technique are considered.