Inversion of the x-ray transform for complexes of lines in \(\mathbb{R}^{n}\) (Q2794613)
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scientific article; zbMATH DE number 6553834
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inversion of the x-ray transform for complexes of lines in \(\mathbb{R}^{n}\) |
scientific article; zbMATH DE number 6553834 |
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10 March 2016
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x-ray transform
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complex of lines
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explicit inversion formula
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integral geometry
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Radon transform
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0.89359176
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0.8914126
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0.88744724
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0.88279533
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0.8810787
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0.8712237
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Inversion of the x-ray transform for complexes of lines in \(\mathbb{R}^{n}\) (English)
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The paper presents a general framework for the explicit inversion of the x-ray transform for both, admissible and non-admissible complexes of lines in an \(n\)-dimensional space. The paper constructs the Radon transform, which is an integral over a hyper-plane from the x-ray transform, i.e. integral over lines. Some examples of exact inversion formulas for admissible and non-admissible complexes of lines are presented. Several theorems are proved.
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