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The objective of the work presented 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 R.R. Schultz and R.L. Stevenson's (1996) MAP estimator. 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.