Abstract
Abstract In this paper, we propose a method for inpainting regular textures composed of oriented patterns and completion of images distorted by long stripes. We have developed a model fit to describe a regular texture as a sum of a few ridge functions. The ridge functions are known in tomography as a result of a back-projection operator applied to projections, or samples of the Radon transform. A computational scheme for the singular value decomposition of a regular texture into the sum of informative ridge functions is presented. The numerical experiments on various images demonstrate the efficiency of the techniques proposed.