Compensation de déformations en tomographie dynamique 3D conique

19 pagesIn dynamic tomography, the measured object or organs are no-longer supposed to be static in the scanner during the acquisition but are supposed to move or to be deformed. Our approach is the analytic deformation compensation during the reconstruction. Our work concentrates on 3D cone beam tomography. We introduce a new large class of deformations preserving the 3D cone beam geometry. We show that deformations from this class can be analytically compensated. We present numerical experiments on phantoms showing the compensation of these deformations in 3D cone beam tomography

Compensation of some time dependent deformations in tomography.

This work concerns 2D + t dynamic tomography. We show that a much larger class of deformations than the affine transforms can be compensated analytically within filtered back projection algorithms in 2D parallel beam and fan beam dynamic tomography. We present numerical experiments on the Shepp and Logan phantom showing that nonaffine deformations can be compensated. A generalization to 3D cone beam tomography is proposed

Échantillonnage efficace en imagerie Doppler

L'objectif de l'échantillonnage efficace est de minimiser le nombre de points de mesures pour la reconstruction d'une image à résolution donnée. L'échantillonnage efficace en tomographie classique est généralisé à la transformée de Radon invariante par rotation dans le cas de fonctions poids polynômiales. Des simulations numériques et l'application à l'imagerie Doppler dans des cas particuliers d'inclinaison de l'étoile, illustrent ce résultat

Compensation de déformations en tomographie dynamique

L'objet de cette étude est la reconstruction tomographique d'objets ou d'organes qui se déforment au cours de l'acquisition des projections dans un scanner. Notre approche est celle de la compensation analytique des déformations lors de la reconstruction par adaptation des algorithmes de type FBP rapides et modernes (contexte de la reconstruction de ROI, Région d'Intérêt). Dans la thèse de Sébastien Roux, des compensations analytiques de déformations affines ont été établies. Nous proposons ici d'étendre ces résultats à des classes de déformations beaucoup plus vastes qui ne conservent que les droites de mesure (et pas nécessairement toutes les droites du plan)

Optimal calibration marker mesh for 2D X-ray sensors in 3D reconstruction.

Image intensifiers suffer from distortions due to magnetic fields. In order to use this X-ray projections images for computer-assisted medical interventions, image intensifiers need to be calibrated. Opaque markers are often used for the correction of the image distortion and the estimation of the acquisition geometry parameters. Information under the markers is then lost. In this work, we consider the calibration of image intensifiers in the framework of 3D reconstruction from several 2D X-ray projections. In this context, new schemes of marker distributions are proposed for 2D X-ray sensor calibration. They are based on efficient sampling conditions of the parallel-beam X-ray transform when the detector and source trajectory is restricted to a circle around the measured object. Efficient sampling are essentially subset of standard sampling in this situation. The idea is simply to exploit the data redundancy of standard sampling and to replace some holes of efficient schemes by markers. Optimal location of markers in the sparse efficient sampling geometry can thus be found. In this case, the markers can stay on the sensor during the measurement with--theoretically--no loss of information (when the signal-to-noise ratio is large). Even if the theory is based on the parallel-beam X-ray transform, numerical experiments on both simulated and real data are shown in the case of weakly divergent beam geometry. We show that the 3D reconstruction from simulated data with interlaced markers is essentially the same as those obtained from data with no marker. We show that efficient Fourier interpolation formulas based on optimal sparse sampling schemes can be used to recover the information hidden by the markers

Algebraic and analytic reconstruction methods for dynamic tomography.

In this work, we discuss algebraic and analytic approaches for dynamic tomography. We present a framework of dynamic tomography for both algebraic and analytic approaches. We finally present numerical experiments

Algorithme rapide de reconstruction tomographique basé sur la compression des calculs par ondelettes

L'introduction de nouveaux systèmes de tomographie 3D à partir de détecteurs multi-lignes ou de détecteurs plats fait augmenter le nombre de données à traiter. De plus, pour certaines applications médicales le temps de reconstruction doit être réduit ( tomofluoroscopie 3D). Nous avons donc développé un nouvel algorithme de reconstruction 3D basé sur la compression des calculs. L'idée principale est d'adapter les techniques de compression à base d'ondelettes à la reconstruction tomographique. Pour cela, nous calculons une transformée en ondelettes indirecte de l'image f à travers la décomposition de ses projections (ou transformée de Radon) Rf. Cette approche est hiérarchique. En effet, nous reconstruisons dans un premier temps, les coefficients d'ondelettes aux échelles grossières, à partir de ces coefficients nous prédisons les coefficients significatifs aux échelles plus fines. Cette prédiction est obtenue en utilisant la structure des "Zerotree" introduite par J. Shapiro dans le cadre de la compression de données. En conclusion notre approche permet de rétroprojeter uniquement les coefficients contenant de l'information pertinante. Elle permet de reconstruire de 2 à 5 fois plus vite que une approche classique FBP (Filtered Back Projection) un volume tomographique (32 x 512 x 512)

Spline driven: high accuracy projectors for tomographic reconstruction from few projections

International audienceTomographic iterative reconstruction methods need a very thorough modeling of data. This point becomes critical when the number of available projections is limited. At the core of this issue is the projector design, i.e., the numerical model relating the representation of the object of interest to the projections on the detector. Voxel driven and ray driven projection models are widely used for their short execution time in spite of their coarse approximations. Distance driven model has an improved accuracy but makes strong approximations to project voxel basis functions. Cubic voxel basis functions are anisotropic, accurately modeling their projection is, therefore, computationally expensive. Both smoother and more isotropic basis functions better represent the continuous functions and provide simpler projectors. These considerations have led to the development of spherically symmetric volume elements, called blobs. Set apart their isotropy, blobs are often considered too computationally expensive in practice. In this paper, we consider using separable B-splines as basis functions to represent the object, and we propose to approximate the projection of these basis functions by a 2D separable model. When the degree of the B-splines increases, their isotropy improves and projections can be computed regardless of their orientation. The degree and the sampling of the B-splines can be chosen according to a tradeoff between approximation quality and computational complexity. We quantitatively measure the good accuracy of our model and compare it with other projectors, such as the distance-driven and the model proposed by Long et al. From the numerical experiments, we demonstrate that our projector with an improved accuracy better preserves the quality of the reconstruction as the number of projections decreases. Our projector with cubic B-splines requires about twice as many operations as a model based on voxel basis functions. Higher accuracy projectors can be used to improve the resolution of the existing systems, or to reduce the number of projections required to reach a given resolution, potentially reducing the dose absorbed by the patient

A B-spline based and computationally performant projector for iterative reconstruction in tomography - Application to dynamic X-ray gated CT

International audienceData modelization in tomography is a key point for iterative reconstruction. The design of the projector starts with the representation of the object of interest, decomposed on a discrete basis of functions. Standard models of projector such as ray driven, or more advanced models such as distance driven, use simple cubic voxels, which result in modelization errors due to their anisotropic behaviour. Moreover approximations made at the projection step increase these errors. Long, Fessler and Balter reduce approximation errors by projecting the cubic voxels more accurately. However anisotropy errors still hold. Spherically symmetric volume elements (blobs) eradicate them, but at the cost of increased complexity. We propose a compromise between these two approaches by using B-splines as basis functions. Their quasi-isotropic behaviour allows to avoid projection inconsistencies, while conserving local influence. Small approximations transform the exact footprint (projection of the basis function) into a separable function, which does not depend on the angle of projection, and is easier and faster to integrate on detector pixels. We obtain a more accurate projector, with no additional computation cost. Such an improvement is particularly of interest in the case of dynamic gated X-ray CT, which can be considered as a tomographic reconstruction problem with very few projection data, and for which we show some preliminary results, with an original method of iterative reconstruction, using spatio-temporal regularization of the "space + time" sequence, and making no use of motion estimation