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

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.

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