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arXiv · 1710.07676

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

Hiroshi Fujiwara·Kamran Sadiq·Alexandru Tamasan
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Abstract

In two dimensions, we consider the problem of inversion of the attenuated $X$-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 $A$-analytic functions in the sense of Bukhgeim.

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Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan. 2017-10-20. Partial inversion of the 2D attenuated $X$-ray transform with data on an arc. https://arxiv.org/abs/1710.07676

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