Filter based MAP estimation of images with integrated segmentation

We present a computationally efficient technique for MAP estimation of images in the presence of both blur and noise. The method uses a piecewise stationary Gaussian prior with the segmentation incorporated in a natural way. To generate the solution we apply the Wiener filter to the data after first subtracting out the influence of the surrounding regions. For any particular segmentation, the method gives rise to a linear system which can be solved using the successive over relaxation (SOR) iterative method. We incorporate the segmentation as an extra, nonlinear step, at each point in the SOR method. The resulting combined method gives a good solution after just a few iterations. The proposed method has wide applicability to inverse imaging problems, and examples are provided showing application to the demosaicking problem.