Far Eastern Mathematical Journal

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A formula for the gradient of the output signal in positron emission tomography


Yarovenko I. P.

2015, issue 1, P. 121-128


Abstract
The work is devoted to the study of qualitative properties for the mathematical model of positron emission tomography. The model is the integral transform of unknown function describing the distribution of activitysources. We propose a formula for the gradient of the output signal. Wegive conditions under which the gradient of the output signal will have a singularity.

Keywords:
radiation transfer theory, positron emission tomography

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References

[1] Visvikis D., Cheze-Le Rest C., Jarritt P., ""PET technology: current trends and future developments"", British J. Radiology, 77:923 (2004), 906-910.
[2] Zaidi H., Montandon M.-L., ""Scatter compensation techniques in PET"", PET Clinics, 2:2 (2007), 219-234.
[3] Kazancev I.G., Jarovenko I.P., Prohorov I.V., “Modelirovanie processa izmerenija komptonovskogo rassejanija v pozitronnoj jemissionnoj tomografii”, Vychislitel'nye tehnologii, 16:6 (2011), 27-37.
[4] Kazancev I.G., Jarovenko I.P., Prohorov I.P., “Analiticheskoe i statisticheskoe modelirovanie formirovanija izobrazhenij rassejannogo izluchenija v jemissionnoj tomografii”, Interjekspo Geo-Sibir', 4 (2011), 94-99.
[5] Chinn G., Foudray A. M. K., Levin C. S., ""A Method to include single photon events in image reconstruction for a 1 mm resolution PET system built with advanced 3-D positioning detectors"", IEEE Nucl. Sci. Symposium (San Diego, 2006), 2007, 1740-1745.
[6] Kosters T., Natterer F., Wubbeling F., ""Scatter correction in PET using the transportequation"", IEEE Nucl. Sci. Symposium (San Diego, 2006), 2007, 3305-3309.
[7] Jarovenko I.P., “Chislennye jeksperimenty s indikatorom neodnorodnosti vpozitronno-jemissionnoj tomografii”, Sibirskij zhurnal industrial'noj matematiki, 2011, № 1, 140-149.
[8] Anikonov D.S., “Postroenie indikatora neodnorodnosti pri radiacionnom obsledovanii sredy”, Doklady RAN, 357:3 (1997), 324-327.
[9] Anikonov D.S., ""Integro-differential indicator of nonhomogenity in tomography problem"", Journal of Inverse and Ill-Posed Problems, 7:1 (1999), 17-59.
[10] Anikonov D.S., ""A formula for the gradient of the transport equation solution"", Journal of Inverse and Ill-Posed Problems, 4:2 (1996), 85-100.
[11] Anikonov D.S., Nazarov V.G., Prohorov I.V., “Vidimye i nevidimye sredy v tomografii”, Doklady Akademii nauk, 357:5 (1997), 599-603.
[12] Konovalova D.S., “Pojetapnoe reshenie obratnoj zadachi dlja uravnenija perenosa primenitel'no k zadache tomografii”, Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki, 49:1 (2009), 189-199.
[13] Konovalova D.S., Prohorov I.V., “Chislennaja realizacija algoritma pojetapnoj rekonstrukcii dlja zadachi rentgenovskoj tomografii”, Sibirskij zhurnal industrial'noj matematiki, 11:4 (2008), 61-65.

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