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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.
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Sadiq et al. (2015) studied this question.
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