5,334 research outputs found
On the -ray transform of planar symmetric 2-tensors
In this paper we study the attenuated -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 -ray data. The characterization is in terms of a Hilbert-transform
associated with -analytic maps in the sense of Bukhgeim.Comment: 1 figure. arXiv admin note: text overlap with arXiv:1411.492
On the range of the Attenuated Radon Transform in strictly convex sets.
In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of A. Bukhgeim. We then uses the range characterization of the Radon transform of functions to characterize the range of the attenuated Radon transform of vector fields as they appear in the medical diagnostic techniques of Doppler tomography. As an application we determine necessary and sufficient conditions for the Doppler and X-ray data to be mistaken for each other. We also characterize the range of real symmetric second order tensor field using the range characterization of the Radon transform of zero tensor field
On the -ray transform of symmetric higher order tensors
In this article we characterize the range of the attenuated and
non-attenuated -ray transform of compactly supported symmetric tensor fields
in the Euclidean plane. The characterization is in terms of a Hilbert-transform
associated with -analytic maps in the sense of Bukhgeim.Comment: 29 pages. arXiv admin note: text overlap with arXiv:1503.0432
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