Partial inversion of the 2D attenuated $ X $-ray transform with data on an arc | Zendy

Hiroshi Fujiwara | Zendy; Kamran Sadiq | Zendy; Alexandru Tamasan | Zendy

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Partial inversion of the 2D attenuated $ X $-ray transform with data on an arc

Author(s) -

Hiroshi Fujiwara,

Kamran Sadiq,

Alexandru Tamasan

Publication year - 2021

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2021047

Subject(s) - mathematics , inversion (geology) , arc (geometry) , hilbert transform , function (biology) , regular polygon , combinatorics , geometry , paleontology , statistics , spectral density , structural basin , evolutionary biology , biology

In two dimensions, we consider the problem of inversion of the attenuated \begin{document}$ X $\end{document} -ray transform of a compactly supported function from data restricted to lines leaning on a given arc. We provide a method to reconstruct the function on the convex hull of this arc. The attenuation is assumed known. The method of proof uses the Hilbert transform associated with \begin{document}$ A $\end{document} -analytic functions in the sense of Bukhgeim.

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