Compensation de déformations en tomographie dynamique 3D conique

Compensation de déformations en tomographie dynamique 3D conique

Compensation of deformations in 3D cone beam tomography

Laurent Desbat Sébastien Roux  Pierre Grangeat 

TIMC-IMAG, In3S, Faculté de Médecine, UJF, 38706, La Tronche, France

Philips Medical Systems Research Paris, 51 rue Carnot, BP 301, 92156 Suresnes Cedex, France

LETI - CEA - DRT, CEA/Grenoble, DTBS, 17 av. des Martyrs, 38054 Grenoble cedex 9, France

Corresponding Author Email: 
Laurent.Desbat@imag.fr
Page: 
461-471
|
Received: 
12 October 2005
|
Accepted: 
N/A
|
Published: 
31 December 2006
| Citation

OPEN ACCESS

Abstract: 

In dynamic tomography, the measured objects 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.

Résumé

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. Nous concentrons ce travail sur la géométrie conique 3D. Nous introduisons une classe de déformations préservant la géométrie conique 3D et nous montrons que les déformations issues de cette classe, beaucoup plus vaste que celle des déformations affines, peuvent être compensées analytiquement. Nous illustrons la compensation de déformations de cette classe par des expérimentations numériques sur des fantômes dynamiques en géométrie conique 3D.

Keywords: 

Dynamic tomography, cone beam, deformation, reconstruction

Mots clés

Tomographie dynamique, géométrie conique, déformation, reconstruction

1. Introduction Et Notations
2. Déformations En Géométrie CB 3D
3. Expérimentations Numériques
4. Discussion
  References

[1] S. BONNET, A. KOENIG, S. ROUX, P. HUGONNARD, R.GUILLEMAUD, and P.GRANGEAT, Dynamic X-ray computed tomography, Proceedings of the IEEE, 91(10):1574--87, October 2003.

[2] C.R. CRAWFORD, K.F. KING, C.J. RITCHIE, and J.D. GODWIN, Respiratory compensation in projection imaging using a magnification and displacement model, IEEE Transactions on Medical Imaging, 15:327-332, 1996.

[3] M.DEFRISE, R.CLACK, and D.TOWNSEND, The solution to the 3D image reconstruction problem from 2D parallel projections, J. Opt. Soc. Am. A, 10:869-877, 1993.

[4] L.DESBAT, M.FLEUTE, M.DEFRISE, X.LIU, C.HUBERSON, R. LAOUAR, R. MARTIN, J. GUILLOU, and S. LAVALLÉE, Minimally Invasive Interventional Imaging for Computer Assisted Orthopedic Surgery, In SURGETICA'2002, pages 288-295, Sauramps médical, 2002.

[5] L. DESBAT AND D. GIRARD, The « minimum reconstructionerror» choice of regularization parameters: some more efficient methods and their application to deconvolution problems.SIAM J. Sci. Comput., 16(6):1387-1403, 1995.

[6] L.DESBAT, S.ROUX, and P.GRANGEAT, Compensation de déformations en tomographie dynamique, In GRETSI 2005 abstract book, page51. (+4 pages sur CD), 2005.

[7] L.DESBAT, S.ROUX, and P.GRANGEAT, Compensation of some time dependent deformations in tomography, submitted to IEEE MI (revision), 2005.

[8] T.FLOHR AND B.OHNESORGE, Heart rate adaptative optimization of spatial and temporal resolution for electrocardiogram-gated multislice spiral CT of the heart, Journal of Computer Assisted Tomography, 25(6):907-923, 2001.

[9] D.A. GIRARD, Asymptotic optimality of the fast randomized versions of GCV and CL in ridge regression and regularisation, Ann. of Stat., 19(4):1950-1963, 1991.

[10] P.GRANGEAT, Analyse d'un sytème d'imagerie 3D par reconstructions à partir de radiographies X en géométrie conique, PhD thesis, ENST, 1987.

[11] P.GRANGEAT, Mathematical framework of cone beam 3{D} reconstruction via the first derivative of the Radon transform, Mathematical Methods in Tomography, G.T. Herman, A.K. Louis, F.Natterer, Lecture Notes in Mathematics, pages 66-97, 1991.

[12] P. GRANGEAT, A. KOENIG, T. RODET, and S. BONNET, Theoretical framework for a dynamic cone-beam reconstruction algorithm based on a dynamic particle model, Phys. Med. Biol., 47(15):2611-2625, August 2002.

[13] M.KACHELRIESS and W.A. KALENDER, Electrocardiogram-correlated image reconstruction from subsecond spiral computed tomography scans of the heart, Medical Physics, 25(12):2417-2431, December 1998.

[14] A.KATSEVICH, Analysis of an exact inversion algorithm for spiral cone beam CT, Phys. Med. Biol., 47:2583-98, 2002.

[15] A.KATSEVICH, Theoretically exact filtered back-projection type inversion algorithm for spiral CT, SIAM. J. Appl. Math.}, 62:2012-26, 2002.

[16] A.KATSEVICH, A general scheme for contructing inversion algorithms for cone beam CT, International journal of Mathematics and Mathematical Sciences, 21:1305-1321, 2003.

[17] F.NOO, M.DEFRISE, R.CLACKDOYLE, and H.KUDO, Image reconstruction from fan-beam projections on less than a short-scan, Phys. Med. Biol., 47: 2525-2546, July 2002.

[18] J.D. PACK and F.NOO, Cone-beam reconstruction using 1d filtering along the projection of m-lines, Inverse Problems} 21(3): 1105-1120, 2005.

[19] S.ROUX, Modèles dynamiques en tomographie. Application à l'imagerie cardiaque, Phd thesis, Université Joseph Fourier, Grenoble 1, France, 2004.

[20] S.ROUX, L.DESBAT, A.KOENIG, and P.GRANGEAT, Efficient acquisition for periodic dynamic CT, IEEE Transactions on Nuclear Sciences, 50(5):1672-77, October 2003.

[21] S. ROUX, L. DESBAT, A. KOENIG, and P. GRANGEAT, Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations, Phys. Med. Biol., 49(11): 2169-82, June 2004.

[22] E.Y SIDKY and X.PAN, A minimum data FBP-type algorithm for image reconstruction in cone-beam CT, In Fully 3D image reconstruction in radiology and medicine proceeding, pages 291-294, Salt Lake City, 2005.

[23] A.SITEK, R.H. HUESMAN, and G.T. GULLBERG, Tomographic iterative reconstruction using unconstrained grids, In Fully 3D image reconstruction in radiology and medicine proceeding, pages 275-278, Salt Lake City, 2005.

[24] J.B. THIBAULT, K.SAUER, C.BOUMAN, and J.HSIEH, Threedimensional statistical modeling for image quality improvements in multi-slice helical CT, In Fully 3D image reconstruction in radiology and medicine proceeding, pages 271-274, Salt Lake City, 2005.

[25] H.K. Tuy, An inversion formula for cone-beam reconstruction, SIAM J. Appl. Math., 43(3):546-552, {1983}.

[26] K.WIESENT, K.BARTH, N.NAVAB, P.DURLAK, T.BRUNNER, O.SCHUETZ, and W.SEISSLER, Enhanced 3-d-reconstruction algorithm for c-arm systems suitable for interventional procedures, IEEE Trans. Med. Imaging, 19(5):391-403, 2000.

[27] Y.ZOU and X.PAN, Image reconstruction on PI-lines by use of filtered backprojection in helical cone-beam CT, Phys. Med. Biol., 49:2717-2731, 2004.