Image inpainting with structural bootstrap priors

In this article, we consider the following inpainting problem arising in image restoration: part of an image has been removed, and we want to restore the image from the remaining, possibly noisy, portion. We show that if the true image contains no sharp edges, the inpainting can be done rather satisfactorily by means of an isotropic smoothness prior assumption. If, on the other hand, we have information concerning discontinuities in the image, we can input this information into the restoration algorithm using an anisotropic smoothness prior. Based on these observations, we propose an inpainting method based on a bootstrapping procedure that consists of the following steps: first, we smooth out the incomplete image and calculate the gradient field. Since this field is smooth, it can be inpainted satisfactorily. By using the inpainted gradient field, we then construct an anisotropic smoothness prior that pilots the inpainting of the original non-smooth image. The calculations are based on the Bayesian interpretation of the inpainting problem as a statistical inverse problem. Keywords: Inpainting; Statistical inversion; Structural priors; Boundary conditions