Abstract. In this paper, we propose a variational framework for computing a superresolved image of a scene from an arbitrary input video. To this end, we employ a recently proposed quadratic relaxation scheme for high accuracy optic flow estimation. Subsequently we estimate a high resolution image using a variational approach that models the image formation process and imposes a total variation regularity of the estimated intensity map. Minimization of this variational approach by gradient descent gives rise to a deblurring process with a nonlinear diffusion. In contrast to many alternative approaches, the proposed algorithm does not make assumptions regarding the motion of objects. We demonstrate good experimental performance on a variety of real-world examples. In particular we show that the computed super resolution images are indeed sharper than the individual input images.