The objective of this work is the super-resolution restoration of a set of images, and we investigate the use of learnt image models within a generative Bayesian framework.It is demonstrated that restoration of far higher quality than that determined by classical maximum likelihood estimation can be achieved by either constraining the solution to lie on a restricted sub-space, or by using the sub-space to define a spatially varying prior. This sub-space can be learnt from image examples.The methods are applied to both real and synthetic images of text and faces, and results are compared to Schultz and Stevenson?s MAP estimator [15]. We consider in particular images of scenes for which the point-to-point mapping is a plane projective transformation which has 8 degrees of freedom. In the real image examples, registration is obtained from the images using automatic methods.