KTH Matematik  

Matematisk Statistik

Tid: 21 april 2008 kl 16.15-17.00

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Prof. Ali Mohammad-Djafari, Paris

Titel: A Gauss-Markov-Potts prior model for images in Bayesian Computed Tomography

Sammanfattning: In many inverse problems in imaging systems and in particular in image reconstruction in Computed Tomography (CT), we may know that the object under the test is composed of a finite number of materials, meaning that, the images to be reconstructed are composed of a finite number of homogeneous compact regions. To account for this prior knowledge, we propose a family of Gauss- Markov fields with hidden region labels field modeled by the Potts Markov field. The marginal distribution of such models are the Gaussian mixture models which have been appropriately used in classification methods.

We use then these prior models in a Bayesian inference framework for imaging inverse problems which give us the possibility to jointly reconstruct the images and segment them in an optimal way. In this talk, first these prior models are presented in details, then appropriate MCMC or variational Bayesian methods are used to compute the mean posterior estimators.

Finally some results are presented to show the efficiency of the proposed methods for different imaging inverse problems, and in particular, in CT with limited angle and number of projections.


Ali Mohammad-Djafari and Lionel Robillard. Hierarchical markovian models for 3D computed tomography in non destructive testing applications. In EUSIPCO 2006. EUSIPCO 2006, September 4-8, Florence, Italy, September 2006.

Hichem Snoussi and Ali Mohammad-Djafari. Estimation of structured Gaussian mixtures: the inverse EM algorithm. IEEE Trans. on Signal Processing, 55(7):3185-3191, July 2007.

Mahieddine Ichir and Ali Mohammad-Djafari. Hidden Markov models for blind source separation. IEEE Trans. on Signal Processing, 15(7): 1887-1899, Jul 2006.

Olivier Féron and Ali Mohammad-Djafari. Image fusion and joint segmentation using an MCMC algorithm. Journal of Electronic Imaging, 14(2):paper no. 023014, Apr 2005. [ bib | http ]

Fabrice Humblot and Ali Mohammad-Djafari. Super-Resolution using Hidden Markov Model and Bayesian Detection Estimation Framework. EURASIP Journal on Applied Signal Processing, Special number on Super-Resolution Imaging: Analysis, Algorithms, and Applications:ID 36971, 16 pages, 2006.

Olivier Féron, Bernard Duchêne, and Ali Mohammad-Djafari. Microwave imaging of piecewise constant objects in a 2D-TE configuration. International Journal of Applied Electromagnetics and Mechanics, 26 (6):167-174, IOS Press 2007.

Olivier Féron, Bernard Duchêne, and Ali Mohammad-Djafari. Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data. Inverse Problems, 21(6):95-115, Dec 2005.

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Sidansvarig: Filip Lindskog
Uppdaterad: 28/02-2008