Error Analysis for Image Inpainting

Image inpainting refers to restoring a damaged image with missing information. In recent years, there have been many developments on computational approaches to image inpainting problem [2, 4, 6, 9, 11–13, 27, 28]. While there are many effective algorithms available, there is still a lack of theoretical understanding on under what conditions these algorithms work well. In this paper, we take a step in this direction. We investigate an error bound for inpainting methods, by considering different image spaces such as smooth images, piecewise constant images and a particular kind of piecewise continuous images. Numerical results are presented to validate the theoretical error bounds.