A Multiresolution Non-Homogeneous MRF Model for Bayesian Tomography

1 The popularity of Bayesian methods in image processing applications has generated a lot of interest in the eld of image modeling. A good image model needs to be non-homogeneous to be able to adapt to the local characteristics of the diierent regions in an image. Toward this end, we propose a non-homogeneous Markov random eld (MRF) model that has space-varying scale parameters. This formulation poses two diiculties: rst, the number of scale parameters to estimate is on the order of the number of pixels in the image. Second, the scale parameters depend on the structure of the underlying image which is unknown. These two diiculties are solved by employing a generalized Gaussian MRF (GGMRF) based image model in a multiresolution framework. While the choice of the GGMRF enables us to estimate the local scale parameters in an intuitive fashion, the multiresolution framework yields two signiicant advantages: rst, it makes it possible to estimate the space-varying scale parameters of the non-homogeneous MRF at any resolution by using the image at the coarser resolution. Second, it yields a multiresolution algorithm that is computationally eecient and more robust than its single resolution counterpart. Since the local scale parameters estimated from the coarser resolution image may over or under estimate the image variation by a xed constant, we introduce a resolution dependent global scaling parameter in the model. These global scaling parameters are estimated directly from the data using the EM algorithm yielding a practical unsupervised reconstruction algorithm. Experimental results on real tomographic data sets demonstrate that the proposed non-homogeneous model and multiresolution reconstruction algorithm is superior to the homogeneous xed resolution model in terms of quality of reconstruction and slightly better in terms of computational eeciency. EDICS number IP 1.6 1 Permission to publish this abstract separately is granted.