A Filtering Approach to Edge Preserving MAP Estimation of Images

The authors present a computationally efficient technique for maximum a posteriori (MAP) estimation of images in the presence of both blur and noise. The image is divided into statistically independent regions. Each region is modelled with a WSS Gaussian prior. Classical Wiener filter theory is used to generate a set of convex sets in the solution space, with the solution to the MAP estimation problem lying at the intersection of these sets. The proposed algorithm uses an underlying segmentation of the image, and a means of determining the segmentation and refining it are described. The algorithm is suitable for a range of image restoration problems, as it provides a computationally efficient means to deal with the shortcomings of Wiener filtering without sacrificing the computational simplicity of the filtering approach. The algorithm is also of interest from a theoretical viewpoint as it provides a continuum of solutions between Wiener filtering and Inverse filtering depending upon the segmentation used. We do not attempt to show here that the proposed method is the best general approach to the image reconstruction problem. However, related work referenced herein shows excellent performance in the specific problem of demosaicing.