Super-resolution Using Bayesian Priors

Abstract

This chapter introduces the use of Bayesian prior image models in the super-resolution reconstruction problem. As seen in Chapter 5, the maximum-likelihood estimator of the super-resolution image is a highly ill-conditioned inverse problem. Consequently, the solution is extremely sensitive to noise in the observed images and to errors in registration. It is notable that, in cases where the ML estimator performs poorly, the resulting super-resolution image does not resemble what we would normally consider a “sensible” image. It is this observation that motivates the Bayesian super-resolution methods described in this chapter. Whereas the ML estimator only considers the conditional likelihood of the observations with respect to the super-resolution image, the Bayesian methods introduce an additional probability density defined a priori over the space of all images. The combined distribution over possible super-resolution images is termed the posterior, and the maximum a posterior (MAP) estimator provides a solution which is both a good fit to the observations, and also has a high likelihood with respect to the prior image model. The image priors considered in this chapter are simple Markov random field (MRF) models, based on heuristic notions about the short-range spatial correlations between pixels in “typical” images.