A new integral transform arising from a theory of imaging based on Compton scattering is introduced and the explicit expression for its inverse is established. Its properties serve as foundation to a new nuclear emission imaging principle.
Une nouvelle transformation intégrale issue de la formation d'image à partir des photons diffusés par effet Compton a été établie. Sa formule d'inversion explicite a été démontrée. Ses propriétés servent de fondement à un nouveau principe d'imagerie nucléaire.
Accepted:
Published online:
Mai K. Nguyen 1; Tuong T. Truong 2
@article{CRMATH_2002__335_2_213_0, author = {Mai K. Nguyen and Tuong T. Truong}, title = {Exact inversion of a compound conical {Radon} transform and a novel nuclear imaging principle}, journal = {Comptes Rendus. Math\'ematique}, pages = {213--217}, publisher = {Elsevier}, volume = {335}, number = {2}, year = {2002}, doi = {10.1016/S1631-073X(02)02453-6}, language = {en}, }
TY - JOUR AU - Mai K. Nguyen AU - Tuong T. Truong TI - Exact inversion of a compound conical Radon transform and a novel nuclear imaging principle JO - Comptes Rendus. Mathématique PY - 2002 SP - 213 EP - 217 VL - 335 IS - 2 PB - Elsevier DO - 10.1016/S1631-073X(02)02453-6 LA - en ID - CRMATH_2002__335_2_213_0 ER -
Mai K. Nguyen; Tuong T. Truong. Exact inversion of a compound conical Radon transform and a novel nuclear imaging principle. Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 213-217. doi : 10.1016/S1631-073X(02)02453-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02453-6/
[1] Radon's problem for some surfaces in , Proc. Amer. Math. Soc., Volume 99 (1987) no. 2, pp. 305-312
[2] Towards direct reconstruction from a gamma-camera based on Compton scattering, IEEE Trans. Med. Imag., Volume 13 (1994) no. 2, pp. 398-407
[3] Transformation de Fourier des Pseudo-fonctions avec Tables de Nouvelles Transformées, CNRS, Paris, 1963
[4] Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, New York, 1966
[5] Apparent image formation by Compton scattered photons in gamma-ray imaging, IEEE Signal Processing Lett., Volume 8 (2001) no. 9, pp. 248-251
[6] On an integral transform and its inverse in nuclear imaging, Inverse Problems, Volume 18 (2002) no. 2, pp. 265-277
[7] Radon Transformation on Real Algebraic Varieties (S. Gindikin; P. Michor, eds.), Proceedings of the Conference “75 Years of Radon Transform”, International Press, Boston, 1994, pp. 252-262
[8] Über die Bestimmung von Funktionnen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten, Ber. Verh. Sachs. Akad. Wiss. Leipzig Math.-Natur. Kl., Volume 69 (1917), pp. 262-277
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