In this work, we propose a new robust and edge-preserving superresolution algorithm to simultaneously estimate all frames of a sequence. The new algorithm is based on the regularized super-resolution approach. In contrast to other multi-frame super-resolution algorithms, the proposed algorithm does not include the motion in the observation model. Instead, transformations caused by the motion are used in the prior model to produce a sequence with improved quality and smoothness in the motion trajectory. We use a Huber norm in the prior term to achieve an algorithm robust to outliers in the motion model while avoiding blurring of edges. The proposed method is significantly more robust than other simultaneous superresolution methods. We provide results to illustrate the performance of the algorithm.