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Some proximal methods for Poisson intensity CBCT and PET
Anthoine 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
CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
39 rue Joliot-Curie 13453 Marseille Cedex 13
2 :  IMB - Institut de Mathématiques de Bordeaux
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
351 cours de la Libération 33405 TALENCE CEDEX
3 :  CPPM - Centre de Physique des Particules de Marseille
CNRS : UMR7346 – IN2P3 – Université de la Méditerranée - Aix-Marseille II
163, avenue de Luminy - Case 902 - 13288 Marseille cedex 09
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.

Inverse Problems and Imaging
Articles dans des revues avec comité de lecture

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

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tomography_global.pdf(1.9 MB)