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 Some proximal methods for Poisson intensity CBCT and PETAnthoine S., Aujol J.-F., Boursier Y., Mélot C.Inverse Problems and Imaging 6, 4 (2012) 1 - http://hal.archives-ouvertes.fr/hal-00640215
Informatique/Traitement des images
Some proximal methods for Poisson intensity CBCT and PET
Sandrine Anthoine ()1, Jean-François Aujol ()2, Y. Boursier ()3, Clothilde Mélot ()1
 1 : LATP - Laboratoire d'Analyse, Topologie, Probabilités http://www.latp.univ-mrs.fr CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III 39 rue Joliot-Curie 13453 Marseille Cedex 13 France 2 : IMB - Institut de Mathématiques de Bordeaux http://www.math.u-bordeaux.fr/IMB/ CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II 351 cours de la Libération 33405 TALENCE CEDEX France 3 : CPPM - Centre de Physique des Particules de Marseille http://marwww.in2p3.fr/ CNRS : UMR7346 – IN2P3 – Université de la Méditerranée - Aix-Marseille II 163, avenue de Luminy - Case 902 - 13288 Marseille cedex 09 France
Cone-Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) are two complementary medical imaging modalities providing respectively anatomic and metabolic information of a patient. In the context of public health, one must address the problem of dose reduction of the potentially harmful quantities related to each exam protocol : X-rays for CBCT and radiotracer for PET. Two demonstrators based on a technological breakthrough (acquisition devices work in photon-counting mode) have been developed and we investigate in this paper the two related tomographic reconstruction problems. We formulate separately the CBCT and the PET problems in two general frameworks that encompass the physics of the acquisition devices and the specific discretization of the object to reconstruct. These objects may be observed from a limited number of angles of views and we take into account the specificity of the Poisson noise. We propose various fast numerical schemes based on proximal methods to compute the solution of each problem. In particular, we show that primal-dual approaches are well suited in the PET case when considering non differentiable regularizations such as Total Variation. Experiments on numerical simulations and real data are in favor of the proposed algorithms when compared with the well-established methods.
Anglais
10/11/2011

Inverse Problems and Imaging
internationale
Articles dans des revues avec comité de lecture
01/01/2012
6
4
1

Tomography – CT – PET – proximal methods – Poisson noise – total variation – wavelet $\ell_1$-regularization.
68U10, 94A08, 47N10
52 pages

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 hal-00640215, version 1 http://hal.archives-ouvertes.fr/hal-00640215 oai:hal.archives-ouvertes.fr:hal-00640215 Contributeur : Jean-François Aujol <> Soumis le : Jeudi 10 Novembre 2011, 23:36:01 Dernière modification le : Lundi 17 Février 2014, 12:54:38