On the $X$-ray transform of planar symmetric 2-tensors

Kamran Sadiq; Otmar Scherzer; Alexandru Tamasan

On the $X$-ray transform of planar symmetric 2-tensors

Analysis of PDEs 2015-03-17 v1

Authors: Kamran Sadiq , Otmar Scherzer , Alexandru Tamasan

Abstract

In this paper we study the attenuated $X$ -ray transform of 2-tensors supported in strictly convex bounded subsets in the Euclidean plane. We characterize its range and reconstruct all possible 2-tensors yielding identical $X$ -ray data. The characterization is in terms of a Hilbert-transform associated with $A$ -analytic maps in the sense of Bukhgeim.

Keywords

X-ray transform attenuated X-ray transform planar symmetric 2-tensors Hilbert transform A-analytic maps range characterization

Cite

@article{arxiv.1503.04322,
  title  = {On the $X$-ray transform of planar symmetric 2-tensors},
  author = {Kamran Sadiq and Otmar Scherzer and Alexandru Tamasan},
  journal= {arXiv preprint arXiv:1503.04322},
  year   = {2015}
}

Comments

1 figure. arXiv admin note: text overlap with arXiv:1411.4923

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