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

Understand

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.