Reconstruction of a Planar Centrally Symmetric Convex Domain by Random Chord Distribution

This paper deals with the classical problems of stochastic tomography: obtaining information about a convex body from the distribution of characteristics of its $$k$$ -dimensional sections. We present a novel approach to reconstructing a planar convex domain from its random oriented chord distribution via recovering the real moments of the domain. Such reconstructions are of interest in many areas of mathematics and in problems of nondestructive evaluation in which one wants to find the shape of an object from measurements mainly from a set of data, such as x-ray projections.