Geodesic
On One Class of Integral Geometry Problems with Incomplete Data
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 46-60

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We consider non-linear problem of reconstruction of multidimensional objects from non-complete data of distant measurements represented in the forms of integral transformations. For the class of $D$-finite objects, with the help of the Prony system, we obtain constructive solutions to these inverse problems.
Keywords: integral transformations, Prony system, $D$-finite functions.
Mots-clés : moments, invisible sets, semi-algebraic domains 
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     title = {On {One} {Class} of {Integral} {Geometry} {Problems} with {Incomplete} {Data}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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D. V. Batenkov; V. P. Golubyatnikov; Y. N. Yomdin. On One Class of Integral Geometry Problems with Incomplete Data. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 46-60. http://geodesic.mathdoc.fr/item/VNGU_2012_12_3_a4/