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arXiv · 2412.18197

The symbol of the normal operator for the d-plane transform on the Euclidean space

Hiroyuki Chihara
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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.

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Hiroyuki Chihara. 2024-12-24. The symbol of the normal operator for the d-plane transform on the Euclidean space. https://arxiv.org/abs/2412.18197

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