On The Range Characterization Of The Two-Dimensional Attenuated Doppler Transform

Keywords

A-analytic maps; Attenuated Doppler transform; Attenuated X-ray transform; Hilbert transform

Abstract

We characterize the range of the attenuated and nonattenuated X-ray transform of compactly supported vector fields in the plane. The characterization is in terms of a Hilbert transform associated with the A-analytic functions à la Bukhgeim. As an application we determine necessary and sufficient conditions for the attenuated Doppler and X-ray data to be mistaken for each other.

Publication Date

1-1-2015

Publication Title

SIAM Journal on Mathematical Analysis

Volume

47

Issue

3

Number of Pages

2001-2021

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/140984282

Socpus ID

84940378098 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84940378098

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