Resolution in dynamic emission tomography

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 5, 2000, Pages 1100-1120

  Maeght, Jean ^a   Noll, Dominikus ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

2 D filtering; 2 D sampling theorem; Aliasing errors; Attenuated Radon transform; Dynamic emission tomography; Photon transport equation; Resolution; Uncertainty principle

Indexed keywords

EID: 0034345316     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098345457     Document Type: Article

References (25)

1. M. ABRAMOWITZ AND I.A. STEGUN, Handbook of Mathematical Functions, Dover, New York, 1970.
2. H.H. BAUSCHKE, D. NOLL, A. CELLER, AND J.M. BORWEIN, An EM-algorithm for Dynamic SPEC Tomography, IEEE Trans. Med. Imag., 18 (1999), pp. 252-261.
3. P.L. BUTZER AND R.J. NESSEL, Fourier Analysis and Approximation, Vol. 1, Birkhäuser-Verlag, Basel, 1971.
4. A. CELLER, T. FARNCOMBE, R. HARROP, AND D. LYSTER, Dynamic heart-in-thorax phantom for functional SPECT, IEEE Trans. Nuclear Sciences, 44 (1997), pp. 1600-1605.
5. A. CELLER, T. FARNCOMBE, R. HARROP, D. NOLL, AND J. MAEGHT, Dynamic SPECT imaging using single camera rotation (dSPECT), IEEE Trans. Nuclear Sciences, 46 (1999), pp. 1055-1061.
6. A. CELLER, A. SITEK, AND R. HARROP, Reconstruction of multiple line source attenuation maps, in IEEE Nuclear Science Symposium Conference Record, IEEE, New York, 1996, pp. 1420-1424.
7. A. CELLER, A. SITEK, E. STOUB, D. LYSTER, C. DYKSTRA, D. WORSLEY, AND A. FUNG, Development of a multiple line source attenuation array for SPECT transmission scans, J. Nuclear Medicine, 38 (1997), p. 215.
8. R. DAUTREY AND J.-L. LIONS, Analyse mathématique et calcul numérique, Tome 9, Masson, Paris, 1984.
9. V. DICKEN, Simultaneous activity and attenuation reconstruction in emission tomography, Inverse Problems, 15 (1999), pp. 931-960.
10. G.T. GULLBERG, R.H. HUESMAN, S.G. ROSS, E.V.R. DI BELLA, G.L. ZENG, B.W. REUTTER, P.E. CHRISTIAN, AND S.A. FORESTI, Dynamic cardiac single photon emission computed tomography, in Nuclear Cardiology: State of the Art and Future Directions, Mosby-Year Book, Philadelphia, in press.
11. A. GJEDDE, Compartmental Analysis, in Principles of Nuclear Medicine, 2nd ed., H.N. Wagner, Jr., Z. Szabo, J.W. Buchanan, Saunders, Philadelphia, PA, 1995, pp. 451-461.
12. C.M. KAO, J.T. YAP, J. MUKHERJEE, M. COOPER, AND C.T. CHEN, An image reconstruction method for dynamic PET, IEEE NSS/MIC Conference Record, IEEE, New York, 1995.
13. H. KRUSE, Resolution of reconstruction methods in computerized tomography, SIAM J. Sci. Stat. Comput., 10 (1989), pp. 447-474.
14. M.A. LIMBER, M.N. LIMBER, A. CELLER, J.S. BARNEY, AND J.M. BORWEIN, Direct reconstruction of functional parameters for dynamic SPECT, IEEE Trans. Nuclear Sciences, 42 (1995), pp. 1249-1256.
15. A. KURUC, Efficient estimation of linear functionals in emission tomography, SIAM J. Appl. Math., 57 (1997), pp. 426-452.
16. J. MAEGHT, D. NOLL, A. CELLER, AND T. FARNCOMBE, Methods for dynamic SPECT, Rapport Interne 99-26, Laboratoire Mathématiques pour l'Industrie et la Physique, 1999. Also available at http://mip.ups.-tlse.fr/publi.
17. K. NAKAJIMA, J. TAKI, H. BUNKO, M. MATSUDAIRA, A. MURAMORI, I. MATSUNARI, K. HISADA, AND T. ICHIHARA, Dynamic acquisition with a three-headed SPECT system: Application of Technetium 99m-SQ30217 myocardial imaging, J. Nuclear Medicine, 32 (1991), pp. 1273-1277.
18. F. NATTERER, Computerized tomography with unknown sources, SIAM J. Appl. Math., 43 (1983), pp. 1201-1212.
19. F. NATTERER, Sampling in fan beam tomography, SIAM J. Appl. Math., 53 (1993), pp. 358-380.
20. F. NATTERER, The Mathematics of Computerized Tomography, Teubner-Verlag, Stuttgart, 1986.
21. F. NATTERER, Determination of tissue attenuation in emission tomography of optically dense media, Inverse Problems, 9 (1993), pp. 731-736.
22. P.A. RATTEY AND A.G. LINDGREN, Sampling the 2-D Radon transform, IEEE Trans. Acoust. Speech Signal Process., 29 (1981), pp. 994-1002.
23. G.N. WATSON, A Treatise on Bessel Functions, Cambridge University Press, Cambridge, UK, 1952.
24. A. WELCH, R. CLARK, F. NATTERER, AND G.T. GULLBERG, Toward accurate attenuation correction in SPECT without transmission measurements, IEEE Trans. Med. Imag., 16 (1997), pp. 532-541.
25. R.G. WELLS, A. CELLER, AND R. HARROP, Analytic calculation of photon distribution in SPECT projections, IEEE Trans. Nuclear Sciences, 45 (1998), pp. 3202-3214.