Geodesic
A formula for the gradient of the output signal in positron emission tomography
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 121-128.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 activity sources. We propose a formula for the gradient of the output signal. We give conditions under which the gradient of the output signal will have a singularity. 
@article{DVMG_2015_15_1_a10,
     author = {I. P. Yarovenko},
     title = {A formula for the gradient of the output signal in positron emission tomography},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {121--128},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a10/}
}
TY  - JOUR
AU  - I. P. Yarovenko
TI  - A formula for the gradient of the output signal in positron emission tomography
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2015
SP  - 121
EP  - 128
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a10/
LA  - ru
ID  - DVMG_2015_15_1_a10
ER  - 
%0 Journal Article
%A I. P. Yarovenko
%T A formula for the gradient of the output signal in positron emission tomography
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2015
%P 121-128
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a10/
%G ru
%F DVMG_2015_15_1_a10
I. P. Yarovenko. A formula for the gradient of the output signal in positron emission tomography. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 121-128. http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a10/

[1] Visvikis D., Cheze-Le Rest C., Jarritt P., “PET technology: current trends and future developments”, British J. Radiology, 77:923 (2004), 906–910 | DOI

[2] Zaidi H., Montandon M.-L., “Scatter compensation techniques in PET”, PET Clinics, 2:2 (2007), 219–234 | DOI | MR

[3] Kazantsev I.G., Yarovenko I.P., Prokhorov I.V., “Modelirovanie protsessa izmereniya komptonovskogo rasseyaniya v pozitronnoi emissionnoi tomografii”, Vychislitelnye tekhnologii, 16:6 (2011), 27-37 | MR

[4] Kazantsev I.G., Yarovenko I.P., Prokhorov I.P., “Analiticheskoe i statisticheskoe modelirovanie formirovaniya izobrazhenii rasseyannogo izlucheniya v emissionnoi tomografii”, Interekspo 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), IEEE, N.Y., 2007, 1740–1745

[6] Kosters T., Natterer F., Wubbeling F., “Scatter correction in PET using the transport equation”, IEEE Nucl. Sci. Symposium (San Diego, 2006), IEEE, N.Y., 2007, 3305–3309

[7] Yarovenko I.P., “Chislennye eksperimenty s indikatorom neodnorodnosti v pozitronno-emissionnoi tomografii”, Sibirskii zhurnal industrialnoi matematiki, 2011, no. 1, 140-149 | MR | Zbl

[8] Anikonov D.S., “Postroenie indikatora neodnorodnosti pri radiatsionnom 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. | DOI | MR | Zbl

[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 | MR | Zbl

[11] Anikonov D.S., Nazarov V.G., Prokhorov I.V., “Vidimye i nevidimye sredy v tomografii”, Doklady Akademii nauk, 357:5 (1997), 599-603 | MR | Zbl

[12] Konovalova D.S., “Poetapnoe reshenie obratnoi zadachi dlya uravneniya perenosa primenitelno k zadache tomografii”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 49:1 (2009), 189-199 | MR | Zbl

[13] Konovalova D.S., Prokhorov I.V., “Chislennaya realizatsiya algoritma poetapnoi rekonstruktsii dlya zadachi rentgenovskoi tomografii”, Sibirskii zhurnal industrialnoi matematiki, 11:4 (2008), 61-65 | MR | Zbl