On the smoothing property of the Bayes approach to picture reconstruction

Abstract

The paper is concerned with the reconstruction of a picture density f from a finite number of its strip integrals. It is shown that the Bayes estimate for f is in the Sobolev space H^{3/2} if the isotropic exponential model for f is used. As picture densities are far from being in H^{3/2} (the isotropic exponential model e.g. implies, roughly speaking, only fin H^{1/2}), the Bayes approach can be expected to smooth out peaks and high contrasts. This drawback of the Bayes approach was in fact observed in a comparative numerical test carried out by Herman and Lent [ 6].