Bayesian image deblurring and boundary effects

We consider the deconvolution problem of estimating an image from a noisy blurred version of it. In particular, we are interested in the boundary effects: since the convolution operator is non-local, the blurred image depend on the scenery outside the field of view. Ignoring this dependency leads to image distortion known as boundary effect. In this article, we consider two different approaches to treat the non-locality. One is to estimate the image extended outside the field of view. The other is to treat the influence of the out of view scenery as boundary clutter. Both approaches are considered from the Bayesian point of view. 1. DEBLURRING PROBLEM Consider the inverse problem of deblurring an image from noisy data. The continuous model for a noisy observation of a blurred image can be written as g(t) = A(t, s)f(s)ds + e(t), t ∈ Q, (1