This paper deals with the problem of reconstructing probabilistic distributions of random functions, which describe images dynamically formed in tomographic experiments. For a certain class of random functions, a reconstruction method is developed. Stability properties of the proposed method are studied.
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V. G. Ushakov and N. G. Ushakov, “Reconstruction of probabilistic characteristics of multivariate random functions from their projections,” Vestn. Mosk. Univ. Ser. 15, Vychisl. Matem. Kibern., No. 4, 32–39 (2001).
O. V. Shestakov, “On the uniqueness of reconstruction of probabilistic characteristics of multivariate random functions from probabilistic characteristics of their projections,” Vestn. Mosk. Univ. Ser. 15, Vychisl. Matem. Kibern., No. 3, 37–41 (2003).
O. V. Shestakov, “An algorithm to reconstruct probabilistic distributions of multivariate random functions from the distributions of their projections,” J. Math. Sci., 112, No. 2, 4198–4204 (2002).
I.N. Troitskiy, Statistical Theory of Tomography [in Russian], Radio i Svyaz, Moscow (1989).
G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers, McGraw–Hill, New York (1968).
A. K. Louis and F. Natterer, “Mathematical problems of computerized tomography,” Proc. of the IEEE, 71, 379–389 (1983).
A.N. Tikhonov and V.Y. Arsenin, Solutions of Ill-Posed Problems, Winston, New York (1977).
*Research supported by the Russian Foundation for Basic Research, project №01–01–97005.
Proceedings of the XXVI International Seminar on Stability Problems for Stochastic Models, Sovata-Bai, Romania, August 27 – September 2, 2006.
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Shestakov, O.V. Reconstructing Distributions of Multivariate Random Functions under Orthogonal Polynomial Projection Approximation*. J Math Sci 196, 78–83 (2014). https://doi.org/10.1007/s10958-013-1639-4
- Reconstruction Method
- Random Function
- Probabilistic Characteristic
- Exact Reconstruction