Geodesic
Some modifications of the integro-differential indicator of nonhomogeneity for improving of the tomography images
Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 2, pp. 195-209 
A. N. Rozhko. Some modifications of the integro-differential indicator of nonhomogeneity for improving of the tomography images. Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 2, pp. 195-209. http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author of the article investigated one algorithm for a solution of a tomography problem, based on calculation of indicator of inhomogeneity [1], that recovers boundaries of different includions of the domain. Different authors, used special programs [3], constructed internal structure of some domain, ingoing radiation flows and calculated outgoing radiation flows. Used this data and indicator of inhomogeneity, they solved the problem of tomography and reconstructed internal structure of the domain. It was true, that indicator performed very well, when the condition of visibility [1] was satisfied. But in that cases, when the boundaries were close to poor invisible [1], the tomographic images of the domain were not good. Used this information the author had to improve investigated indicator. Some images were improved. Some modifications are presented in this article.

[1] D. S. Anikonov, “Integro-differential indicator of nonhomogeneity problem”, Journal of Inverse and Ill-Posed Problems, 7:1 (1999), 17–59 | DOI | MR | Zbl

[2] F. Natterer, Matematicheskie aspekty kompyuternoi tomografii, Per. s angl., Mir, M., 1990, 288 pp. | MR | Zbl

[3] D. S. Anikonov, A. E. Kovtanyuk, I. V. Prokhorov, Ispolzovanie uravneniya perenosa v tomografii, Logos, M., 2000, 169–182

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[6] V. G. Nazarov, Chislennye eksperimenty v tomografii s ispolzovaniem indikatora neodnorodnosti i mery vidimosti, Preprint No 16 DVO RAN. Institut prikladnoi matematiki, Dalnauka, Vladivostok, 1997, 15 pp.

[7] V. G. Nazarov, “Ob odnom sposobe povysheniya kontrastnosti tomogramm”, Tezisy dokladov dalnevostochnoi matematicheskoi shkoly-seminara imeni akademika E. V. Zolotova, 2001, 55–56

[8] A. N. Rozhko, “Primenenie veivlet-analiza dlya uluchsheniya svoistv chislennogo differentsirovaniya”, Tezisy matematicheskoi nauchnoi konferentsii studentov i aspirantov po matematicheskomu modelirovaniyu DVGU, 2001, 94–96