On the Range Characterization of the two dimensional attenuated Doppler\n Transform

2014/11/18 by Kamran Sadiq, Sadiq, Kamran, Alexandru Tamasan +1 · 2 citations
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1411.4923

openalex publication_date 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the range of the attenuated and non-attenuated X-ray\ntransform of compactly supported vector fields in the plane. The\ncharacterization is in terms of a Hilbert transform associated with the\nA-analytic functions `a la Bukhgeim. As an application we determine\nnecessary and sufficient conditions for the attenuated Doppler and X-ray data\nto be mistaken for each other.\n

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