ON ASYMPTOTIC EFFICIENCY IN A PROBLEM OF TOMOGRAPHY

Consider the model of X-ray tomography, where we observe the Radon tra nsform Rf of a function f on R-N with additive Gaussian white noise. W e assume that f belongs to a class of functions with exponentially dee r-easing Fourier transforms. We construct an estimator of the function f that converges with the optimal I-ate, in the sense of minimax, on this class, and which is, moreover, asymptotically efficient: it attai ns the best constant in asymptotics of the minimax risk.