In multiple-image super-resolution, a high resolution image is estimated from a number of lower-resolution images. This involves computing the parameters of a generative imaging model (such as geometric and photometric registration, and blur) and obtaining a MAP estimate by minimizing a cost function including an appropriate prior. We consider the quite general geometric registration situation modelled by a plane projective transformation, and make two novel contributions: (i) in previous approaches the MAP estimate has been obtained by fir st computing and fixing the registration, and then computing the super-re solution image with this registration. We demonstrate that superior estim ates are obtained by optimizing over both the registration and image; (ii) the parameters of the edge preserving prior are learnt automatically from the data, rather than being set by trial and error. We show examples on a number of real sequences including multiple stills, digital video, and DVDs of movies.