Optimal Rates of Convergence of Estimates in the Stochastic Problem of Computerized Tomography

We consider the stochastic tomography problem, i.e., reconstruction of an unknown image from observations of its integrals over hyperplanes (lines in the two-dimensional case) in the presence of random noise. The minimax lower bound on image reconstruction accuracy is established in classes of smooth functions. An image estimation method is proposed which achieves this bound by the order of rate of convergence.