**DROITE Workshop**

**08/06/2012
MESR Paris
**

**(25 rue de la Montagne Ste Genevieve, Paris V, salle JA 05)**

** Maths of Tomography, Medical Imaging and HPC: Program**

** ATTENTION inscription obligatoire avant lundi 28 mai minuit car le nombre de places est limité
**

** Participants :
Julien Bert, PhD, LaTIM - INSERM - UMR 1101 ;
Rolf Clackdoyle, DR CNRS, LHC St Etienne ;
Claude Comtat, CEA Saclay ;
Michel Defrise, Univ Libre de Bruxelles ;
Laurent Desbat, UJF and MESR/DGRI/SSRI/A3 ;
EL OTMANI Mohamed, collaborateur ESRF, univ MAROC ;
EL MOUTAOUAKKIL Abdelmajid, ESRF ;
Catherine Burnier-Menessier, CPE Lyon et LHC (UJM) ;
Johan Nuyts, KU Leuven, Belgique ;
Thomas Rodet, SUPELEC et Univ de Paris Sud ;
Simon Stute, CEA Saclay
**

** 13h00: Welcome, salle JA 05, MESR
**

** 13h15:
The use of local physicals models for iterative reconstruction of CT.
Johan Nuyts, Katrien Van Slambrouck, Koen Michielsen.
**

Metal objects often cause severe streak artifacts in CT reconstruction. The state-of-the-art method to reduce these artifacts is the so-called projection-completion method, where the metal projections are replaced with synthetic data that do not give rise to such artifacts. However, removal of the projections through the metal(s) eliminates also some valid information, and as a result, new artifacts are often observed near the metal objects. We attempt to reduce the metal artifacts by better modeling the physics, such that it is no longer necessary to remove projection data. Because beam hardening is a major contributor to metal artifacts, we model the energy dependent behavior of CT attenuation. The more complex model makes the already slow iterative reconstruction even slower. To reduce the computational burden, we divide the image in patches, and use an appropriate model in each patch. The expensive polychromatic model is only applied in small patches containing metals, while a simpler "water correction" model is used everywhere else. The patches are updated sequentially, which results in a considerable acceleration of convergence (an extreme example are coordinate ascent algorithms, which are known to converge much faster than simultaneous update methods). We are applying this patch-work approach also in breast tomosynthesis, to accelerate the reconstruction and to implement a position dependent resolution model. Studies with human and computer observers indicate that iterative reconstruction with resolution model can improve detection and shape discrimination of micro-calcifications.

** 14h15:
Evolutive coronal structures imaging, Variational Bayesian approach for tomography with source separation problem.
Thomas Rodet, Supelec et Université d'Orsay.
**

In this work, we propose to reconstruct the 3D structure of the solar atmosphere, taking into account the temporal evolution of the coronal structures. To do this we develop a new method, which considers that the object of interest consists of several sources each one having different evolution from the other at different time. The data are the Radon transform of an instantaneous mixture of sources. So, we must solve a source separation problem with a linear mixture of sources. To our best knowledge, this problem is still open. To solve this problem of source separation, we have introduced a sparsity information on the sources, and we have chosen to use the variational Bayesian approach for reduce the computation time.

** 15h15:
Practical considerations for image-based PSF and blobs reconstructions in PET.
Simon Stute, CEA Saclay.
**

In PET, the image spatial resolution and noise properties strongly depend on the accuracy of the system matrix model used in the iterative reconstruction. An image-based model of the point-spread function (PSF) is not the most accurate one, but is still of great interest: it is easy to implement and leads to computation times fully tractable in clinical routine. In another hand, any system matrix modeling that is closed to the reality leads to very ill-conditioned inverse problems. In that context, the recursive inversion of the problem produces ringing artifacts in the image, called the Gibbs artifacts. We study all different practical aspects of doing iterative reconstructions using an image-based model of the PSF. We first determine the different origins of the Gibbs artifact, and then propose a solution related to the Sieves theory that ensures a better noise/spatial resolution compromise than the methods used in clinics, but also an image free from Gibbs artifacts. We also study the way the image-based PSF coupled to the geometric projector should be chosen.

*This
DROITE workshops are supported by a grant from << Région
Rhône Alpes>> (ARC
6, T.I.C. et Usages Informatiques Innovants) *

This workshop is supported by the labex CAMI and the ECCAMI project.