Revisiting the Problem of Recovering Functions in ${\mathbb{R}}^n$ 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 $\Bbb R^{n}$where$1\leq k\leq n - 2$\mathrm{.}Forthesevaluesof$k$ the dimension of the set $\mathcal{H}(n,k)$, of all $k$ dimensional planes in ${\mathbb{R}}^n$, is greater than $n$ and thus in order to obtain a well-posed problem one should choose proper subsets of $\mathcal{H}(n,k)$. We present inversion methods for some prescribed subsets of $\mathcal{H}(n,k)$ which are of dimension $n$.