Inversion of the attenuated Radon transform (Q2709873)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inversion of the attenuated Radon transform |
scientific article |
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Inversion of the attenuated Radon transform (English)
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20 February 2002
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Radon transform
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single photon emission tomography
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inversion formula
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filtered backprojection algorithm oscillators
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Hilbert transform
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numerical experiments
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The author proves an inversion formula for the attenuated Radon transform in the two-dimensional plane similar to one given by \textit{Novikov} [preprint, CNRS, UMR 6629, Dep. Math., Univ. Nantes]. The proof uses tools which the author developed in some earlier work studying the range of the attenuated Radon transform. The inversion formula is given in form of a divergence expression of a spherical integral related to the Hilbert transform. The paper further gives an outline for an algorithmic approach which assumes some usual sampling conditions. Numerical experiments have been done using an elliptical chest phantom.
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