Inversion of the Attenuated X-Ray Transforms: Method of Riesz Potentials

The attenuated X-ray transform arises from the image reconstruction in single-photon emission computed tomography. The theory of attenuated X-ray transforms is so far incomplete, and many questions remain open. This paper is devoted to the inversion of the attenuated X-ray transforms with nonnegativ...

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Bibliographic Details
Published inJournal of function spaces Vol. 2020; no. 2020; pp. 1 - 7
Main Author Yufeng, Yu
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
Hindawi Limited
Wiley
Subjects
Aircraft
Analysis
Attenuation
CAT scans
Computed tomography
Construction planning
Diagnostic imaging
Image processing
Image reconstruction
Inversion
Methods
Photon emission
Single photon emission computed tomography
Symmetry
Tomography
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Summary:The attenuated X-ray transform arises from the image reconstruction in single-photon emission computed tomography. The theory of attenuated X-ray transforms is so far incomplete, and many questions remain open. This paper is devoted to the inversion of the attenuated X-ray transforms with nonnegative varying attenuation functions μ, integrable on any straight line of the plane. By constructing the symmetric attenuated X-ray transform Aμ on the plane and using the method of Riesz potentials, we obtain the inversion formula of the attenuated X-ray transforms on Lpℝ21≤p<2 space, with nonnegative attenuation functions μ, integrable on any straight line in ℝ2. These results are succinct and may be used in the type of computerized tomography with attenuation.
ISSN:2314-8896
2314-8888
DOI:10.1155/2020/5896328