Model distortions in Bayesian MAP reconstruction

The Bayesian approach and especially the maximum aposteriori (MAP) estimator is most widely used to solve variousproblems in signal and image processing, such as denoising anddeblurring, zooming, and reconstruction. The reason is that itprovides a coherent statistical framework to combine observed(noisy) data with prior information on the unknown signal or imagewhich is optimal in a precise statistical sense. This paperpresents an objective critical analysis of the MAP approach. Itshows that the MAP solutions substantially deviate from both thedata-acquisition model and the prior model that underly the MAPestimator. This is explained theoretically using severalanalytical properties of the MAP solutions and is illustratedusing examples and experiments. It follows that the MAP approachis not relevant in the applications where the data-observation andthe prior models are accurate. The construction of solutions(estimators) that respect simultaneously two such models remainsan open question.