Abstrakt

Revisiting the problem of recovering functions in ℝⁿ by integration on k Dimensional planes

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 , 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 . We present inversion methods for some prescribed subsets of which are of dimension n.