On Y. Nievergelt's inversion formula for the Radon transform

TL;DR

This paper extends Y. Nievergelt's inversion formula for the Radon transform from lines in the plane to the k-plane Radon transform in higher dimensions, applicable to continuous and L^p functions.

Contribution

It generalizes Nievergelt's inversion method to the k-plane Radon transform in R^n for all 1 ≤ k < n, broadening its applicability.

Findings

Extended inversion formula to higher-dimensional k-plane Radon transforms

Applicable to continuous and L^p functions in R^n

Provides a unified approach for all 1 ≤ k < n

Abstract

We generalize Y. Nievergelt's inversion method for the Radon transform on lines in the 2-plane to the $k$-plane Radon transform of continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$.