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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.18197 |
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| _version_ | 1866915078145572864 |
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| author | Chihara, Hiroyuki |
| author_facet | Chihara, Hiroyuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The symbol of the normal operator for the d-plane transform on the Euclidean space Chihara, Hiroyuki Analysis of PDEs Functional Analysis Primary 58J40, Secondary 53C65 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. |
| title | The symbol of the normal operator for the d-plane transform on the Euclidean space |
| topic | Analysis of PDEs Functional Analysis Primary 58J40, Secondary 53C65 |
| url | https://arxiv.org/abs/2412.18197 |