The symbol of the normal operator for the d-plane transform on the Euclidean space
Analysis of PDEs
2024-12-25 v1 Functional Analysis
Abstract
We directly compute the symbol of the normal operator for the d-plane transform on the Euclidean space. We show that this symbol is the product of the symbol of the power of the Laplacian of order -d/2 and a constant given by an invariant integral over excess-dimensional spaces. This leads to an alternative derivation of the filtered backprojection formula for the d-plane transform.
Cite
@article{arxiv.2412.18197,
title = {The symbol of the normal operator for the d-plane transform on the Euclidean space},
author = {Hiroyuki Chihara},
journal= {arXiv preprint arXiv:2412.18197},
year = {2024}
}
Comments
5 pages, no figure