On the amount of regularization for super-resolution interpolation

Super-resolution (SR) aims at combining several aliased images of the same scene into a higher resolution image by using the difference in sampling caused by camera motion. As the problem of SR is generally ill-posed, techniques developed in the literature often rely on hypotheses on the regularity of the image. In this paper, we try to minimize these assumptions for the interpolation part of super-resolution. We describe situations where SR interpolation is invertible and/or well conditioned. We first study the interpolation problem for large numbers of images, when motions are pure translations. Then, we look at the more generic problem of superresolution interpolation with translations and rotations. We give a simple condition on the number of images and zoom factor for perfect recovery of the high resolution image. We also study the conditioning in the critical case and propose a regularization method which adapts to local sampling variations.