A perceptual Bayesian estimation framework and its application to image denoising

We present a generic Bayesian framework for signal estimation that incorporates into the cost function a perceptual metric. We apply this framework to image denoising, considering additive noise of known density. Under certain assumptions on the way local differences in visual responses add up into a global perceptual distance, we obtain analytical solutions that exhibit interesting theoretical properties. We demonstrate through simulations, using an infomax nonlinear perceptual mapping of the input and a local Gaussian model, that in the absence of a prior the new solutions provide a significant improvement on the visual quality of the estimation. Furthermore, they also improve in Mean Square Error terms w.r.t. their non-perceptual counterparts.