Inversion of the k-plane transform by orthogonal function series expansions

Abstract

The k-plane transform encompasses both the X-ray and Radon transforms. A series inversion which operates in the unified setting of the k-plane transform is presented. The author shows that with respect to either the Jacobi or the associated Laguerre polynomial bases for square integrable point functions, the k-plane transform assumes a block-diagonal-like form. Additionally, estimates are given for the minimum number of discretely sampled direction sets at which the k-plane transform must be known in order to recover a point function up to a given degree.