Open AccessPartial inversion of the 2D attenuated $ X $-ray transform with data on an arc
Author(s) -
Hiroshi Fujiwara,
Kamran Sadiq,
Alexandru Tamasan
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021047
Subject(s) - inversion (geology) , mathematics , arc (geometry) , hilbert transform , function (biology) , regular polygon , combinatorics , algorithm , arithmetic , geometry , geology , paleontology , statistics , spectral density , structural basin , evolutionary biology , biology
In two dimensions, we consider the problem of inversion of the attenuated \begin{document}$ 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.