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. 
@article{SJIM_2014_17_3_a9,
     author = {V. G. Romanov},
     title = {Recovering jumps in {X-ray} tomography},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {98--110},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a9/}
}
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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/