A Variational Approach to Image Inpainting and Text Removal

A commonly occurring problem in image processing is the reconstruction of missing data, generally referred to as image inpainting and can be viewed as a 2D interpolation problem. In this paper we present an approach based on variational model to solve the inpainting problem. Previously the total variation model has been successfully used to solve inpainting problems. We introduce a variant of total variation model that includes a parameter q that controls the degree of smoothness of the reconstruction. The corresponding Euler-Lagrange equation is derived and the corresponding boundary value problem solved. Test examples show that the method works well.