Counter-examples for Bayesian MAP restoration

Authors:
Mila Nikolova
Affiliations:
CMLA, ENS Cachan, CNRS, PRES UniverSud, Cachan, France
Venue:
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Year:
2007

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Abstract

Bayesian MAP is most widely used to solve various inverse problems such as denoising and deblurring, zooming, reconstruction. The reason is that it provides a coherent statistical framework to combine observed (noisy) data with prior information on the unknown signal or image. However, this paper exhibits a major contradiction since the MAP solutions substantially deviate from both the data-acquisition model and the prior model. This is illustrated using experiments and explained based on some known analytical properties of the MAP solutions.