Image and signal restoration using pairwise markov trees

PET/CT image denoising and segmentation based on a multi observation and a multi scale Markov tree model

“…Multi modality tumor segmentation was performed by exploiting the hierarchical property of the HMT, allowing associating the high resolution CT image at the leafs of the tree, and the lower resolution PET image at the next higher scale in the tree. Future work will focus on exploiting this HMT model for PET/MR and PET multi tracer information, in addition to the use of Pairwise Markov Tree (PMT) [1] combined with evidence theory [7]. Validation of the PET/CT segmentation on datasets with histopathological reference will be also presented.…”

“…Thanks to its remarkable properties (multi observation and multi resolution joint statistics, as illustrated in Fig. 1) such a model (Hidden Markov Tree, HMT) [1] can provide fast computation, improved robustness and an effective interpretational process when handling the whole observed data simultaneously. The HMT model is defined as follows: let S be a finite set of points and X=(X s ) s S , Y=(Y s ) s S two stochastic processes indexed on S. Each X s takes its values finite set of classes Ω={ω 1,.., ω k } and Y s takes its values in the set of observations (real values).…”

A Recursive Model-Reduction Method for Approximate Inference in Gaussian Markov Random Fields

“…2 2) Entropy and Fisher Information in Chordal GMRFs: Based on (7), it follows that the entropy of a chordal MRF likewise decomposes in terms of marginal entropy on the cliques and separators of . In the moment parameters of the GMRF, we have (9) where and denote marginal entropy of cliques and separators, computed using performing the conversion (8). Thus, both and can be computed with complexity.…”

“…3 Starting from , we compute a sequence using Newton's method. For each , this requires solving the linear system (14) where is the principle submatrix of corresponding to and is the corresponding subvector of computed using (8). We then set , where is determined by back-tracking line search to stay within and to insure that entropy is increased.…”

“…8 We model SSHA by the thin-membrane model, which seems an appropriate choice as it favors a level sea-surface. We estimate SSHA at the vertices of an 800 2400 lattice covering latitudes between and a full 360 of longitude, which yields a resolution of in both latitude and longitude.…”