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We consider non parametric estimation problem for stochastic tomographyregression model, i.e. we consider the estimation problem of function ofmultivariate variables (image) observed through its Radon transformationcalculated with the random errors. For this problem we develop a new adaptivemodel selection method. By making use the Galtchouk and Pergamenshchikovapproach we construct the model selection procedure for which we show a sharpnon asymptotic oracle inequality for the both usual and robust quadratic risks,i.e. we show that the proposed procedure is optimal in the oracle inequalitiessense.

Sharp non asymptotic oracle inequalities for non parametric computerized tomography model