MELOT, Clothilde; BOURSIER, Yannick; AUJOL, Jean-François; ANTHOINE, Sandrine

doi:10.3934/ipi.2012.6.565

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MELOT, Clothilde
Institut de Mathématiques de Marseille [I2M]

BOURSIER, Yannick
Centre de Physique des Particules de Marseille [CPPM]

AUJOL, Jean-François
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Inverse Problems and Imaging. 2012-11, vol. 6, n° 4, p. p. 565-598

AIMS American Institute of Mathematical Sciences

Résumé en anglais

Cone-Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) are two complementary medical imaging modalities providing respectively anatomic and metabolic information on 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. It turns out that in this low-dose context, i.e. for low intensity signals acquired by photon counting devices, noise should not be approximated anymore by a Gaussian distribution, but is following a Poisson distribution. 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. 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 well-established methods.< Réduire

Mots clés en anglais

wavelet $\ell_1$-regularization

Tomography

total variation

Poisson noise

proximal methods

PET

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189954

DOI

http://dx.doi.org/10.3934/ipi.2012.6.565

Project ANR

Adaptivité pour la représentation des images naturelles et des textures - ANR-08-EMER-0009

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251