F. O. Goncharov, R. G. Novikov, “An analog of Chang inversion formula for weighted Radon transforms in multidimensions”, Eurasian Journal of Mathematical and Computer Applications, 2016, том 4, выпуск 2,страницы 23

An analog of Chang inversion formula for weighted Radon transforms in multidimensions

F. O. Goncharov^ab, R. G. Novikov^cd

^a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141700, Russian Federation
^b Institute for Information Transmission Problems (RAS), Bolshoy Karetny per. 19, buld.1, Moscow 127051, Russian Federation
^c CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau, France;
^d Institute of Earthquake Prediction Theory and Mathematical Geophysics (RAS), 117997 Moscow, Russia;

Аннотация: In this work we study weighted Radon transforms in multidimensions. We inсtroduce an analog of Chang approximate inversion formula for such transforms and describe all weights for which this formula is exact. In addition, we indicate possible tomographical applications of inversion methods for weighted Radon transforms in 3D.

Ключевые слова: weighted Radon transforms, inversion formulas.

MSC: 44A12, 65R32

Поступила в редакцию: 20.04.2016

Язык публикации: английский