Geodesic
Recovering jumps in X-ray tomography
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 98-110.

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The problem of finding the boundaries of the discontinuities and the jumps of a piecewise smooth function is considered for X-ray fan tomography. An algorithm of the reconstruction of unknown values and explicit formulas for their calculation are given. The original problem of X-ray tomography is reduced to a problem for a continuous piecewise differentiable function.
Keywords: tomography, determination of discontinuity lines, stability, uniqueness. 
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V. G. Romanov. Recovering jumps in X-ray tomography. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 98-110. http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a9/

[1] Anikonov D. S., “Integro-differential heterogeneity indicator in tomography problem”, J. Inverse Ill-Posed Probl., 7:1 (1999), 17–59 | DOI | MR | Zbl

[2] Anikonov D. S., “Indikator kontaktnykh granits dlya odnoi zadachi integralnoi geometrii”, Sib. mat. zhurn., 49:4 (2008), 739–755 | MR | Zbl

[3] Anikonov D. S., Konovalova D. S., “Zadacha integralnoi geometrii o neizvestnoi granitse dlya puchka pryamykh”, Sib. mat. zhurn., 52:5 (2011), 972–976 | MR

[4] Anikonov D. S., Balakina E. Yu., “Polikhromaticheskii indikator neodnorodnosti neizvestnoi sredy dlya zadachi rentgenovskoi tomografii”, Sib. mat. zhurn., 53:4 (2012), 721–740 | MR | Zbl

[5] Vainberg E. N., Kazak I. A., Faingoiz M. L., “Rentgenovskaya vychislitelnaya tomografiya po metodu obratnogo proetsirovaniya s filtratsiei dvoinym differentsirovaniem”, Defektoskopiya, 1985, no. 2, 31–39

[6] Faridani A., Keinert F., Natterer F., Ritman T. L., Smith K. T., “Local and global tomography”, Signal processing, 23 (1990), 241–255 | DOI | MR | Zbl

[7] Katsevich A. I., Ramm A. G., “New methods for finding values of the jumps of a function from its local tomographic data”, Inverse Problems, 11 (1995), 1005–1023 | DOI | MR | Zbl

[8] Louis A. K., Maass P., “Contour reconstruction in 3-D X-Ray CT”, IEEE Trans. Med. Imag., 12:4 (1993), 109–115 | DOI | MR

[9] Mukhometov R. G., “Zadacha vosstanovleniya dvumernoi rimanovoi metriki i integralnaya geometriya”, Dokl. AN SSSR, 232:1 (1977), 32–35 | MR | Zbl