Computation of unmeasured third-generation VCT views from measured views

IEEE Transactions on Medical Imaging

Volumn 21, Issue 7, 2002, Pages 801-813

  Patch, Sarah K ^a  

^a GE MEDICAL SYSTEMS   (United States)

Author keywords

Range conditions; Tomography

Indexed keywords

COMPUTERIZED TOMOGRAPHY; IMAGE QUALITY; IMAGE RECONSTRUCTION; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

VOLUMETRIC COMPUTED TOMOGRAPHY (VCT);

MEDICAL IMAGING;

ALGORITHM; ARTICLE; COMPUTER SIMULATION; EVALUATION; FOURIER ANALYSIS; IMAGE QUALITY; INSTRUMENTATION; METHODOLOGY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; SPIRAL COMPUTER ASSISTED TOMOGRAPHY; THREE DIMENSIONAL IMAGING; VALIDATION STUDY;

ALGORITHMS; COMPUTER SIMULATION; FOURIER ANALYSIS; IMAGING, THREE-DIMENSIONAL; PHANTOMS, IMAGING; RADIOGRAPHIC IMAGE ENHANCEMENT; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; TOMOGRAPHY, SPIRAL COMPUTED;

EID: 0036628474     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2002.801164     Document Type: Article

References (16)

1. F. John, "The ultrahyperbolic equation with 4 independent variables," Duke Math. J., pp. 300-322, 1938.
2. S.K. Patch, "Almost-everywhere extrapolation using 2D transforms from cone beam data," U.S. Patent 6 173 030, 2001.
3. L.A. Feldkamp, L.C. Davis, and J.W. Kress, "Practical cone-beam algorithm," JOSA A, vol. 1, no. 6, pp. 612-619, 1984.
4. P. Grangeat, "Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform," in Lecture Notes in Mathematics. Berlin Germany: Springer-Verlag, 1991, Mathematical Methods in Tomography, pp. 66-97.
5. H. Kudo, F. Noo, and M. Defrise, "Cone-beam filtered-backprojection algorithm for truncated helical data," Phys. Med. Biol., vol. 43, pp. 2885-2909, 1998.
6. P.R. Edholm and P.E. Danielsson, "A theorem on divergent projections," in Three-Dimensional Image Reconstruction in Radiation and Nuclear Medicine, P. Grangeat and J.L. Amans, Eds. Dordrecht, The Netherlands: Kluwer Academic, 1996, pp. 35-45.
7. L. Asgiersson, "Ueber eine Mittelwertseigenschaft von Loesungen homogener linearer partieller Differentialgleichungen zweiter Ordnung mit konstanten Koeffizienten," Mathematische Annalen, vol. 13, pp. 321-346, 1938.
8. G. Owens, "An explicit formula for the solution of the ultrahyperbolic equation in four variables," Duke Math J., vol. 9, pp. 272-282, 1942.
9. _, "A boundary-value problem for analytic solutions of an ultrahyperbolic equation," Duke Math J., vol. 20, pp. 29-38, 1953.
10. D. Finch, "Cone beam reconstruction with sources on a curve," SIAM J. Appl. Math., vol. 45, no. 4, pp. 665-673, 1985.
11. J. Chen, "A theoretical framework of regional cone-beam tomography," IEEE Trans. Med. Imag., vol. 11, pp. 342-350, Sept. 1992.
12. K. Tam, "Method and system for processing cone beam data for reconstructing free of boundary-induced artifacts a three dimensional computerized tomography image," US Patent 5 390 111, 1993.
13. J. Hu, C. Ingrassia, S. Lowitzsch, J. Park, A. Pineda, D. Reynolds, and N. Valdivia, "Second-order solution of Fritz John's ultrahyperbolic PDE for volumetric computed tomography," in Final Rep. IMA Summer Student Workshop Mathematical Modeling, 2000.
14. F. John, Partial Differential Equations. Berlin, Germany: Springer-Verlag, 1982.
15. A.A. Kirillov, "On a problem of I.M. Gelfand," Sov. Doklady, pp. 268-269.
16. H.K. Tuy, "An inversion formula for cone-beam reconstruction," SIAM J. Appl. Math., vol. 43, pp. 546-552, 1983.