Revisiting the Problem of Recovering Functions in Rⁿ by Integration on k Dimensional Planes

الأصل · EN

The aim of this paper is to present inversion methods for the classical Radon transform which is defined on a family of k dimensional planes in Rⁿ where 1≤ k≤ n - 2. For these values of k the dimension of the set H(n,k), of all k dimensional planes in Rⁿ, is greater than n and thus in order to obtain a well-posed problem one should choose proper subsets of H(n,k). We present inversion methods for some prescribed subsets of H(n,k) which are of dimension n.