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

2017/10/20 by Fujiwara, Hiroshi, Sadiq, Kamran, Tamasan, Alexandru · 1 citation
#30E20 #35J56 #45E05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.07676

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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