Optimal convergence rates of estimates in probabilistic statement of tomography problem

The probabilistic statement of tomography problem, i.e. unknown image restoration based on observation of integrals on hyperplanes in the presence of random uncorrelated noise is considered. The accuracy of the image estimate is measured by the value of maximum average risk with respect to square and modulus loss functions. The lower bound for normalized average risk of any estimate and the upper bound for average risk of some estimates are found. These results enable to determine optimal convergence rates and asymptotically minimax accuracy of image restoration for the class of smooth functions (images).