On the X-ray transform of planar symmetric 2-tensors
Copyright policy )On the X-ray transform of planar symmetric 2-tensors
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
- Austrian Academy of Sciences Austria
- Johann Radon Institute for Computational and Applied Mathematics Austria
- University of Vienna Austria
- University of Central Florida United States
101028 Mathematical modelling, X-ray transform of symmetric tensors, Inverse problems for PDEs, Hilbert transform, boundary rigidity problem, Mathematics - Analysis of PDEs, FOS: Mathematics, Boundary rigidity problem, INVERSION-FORMULA, Radon transform, A-analytic maps, RANGE CHARACTERIZATION, SURFACES, Systems of linear first-order PDEs, \(X\)-ray transform of symmetric tensors, DOPPLER TRANSFORM, \(A\)-analytic maps, TENSOR TOMOGRAPHY, attenuated \(X\)-ray transform, 101028 Mathematische Modellierung, Special integral transforms (Legendre, Hilbert, etc.), Attenuated X-ray transform, ATTENUATED RADON-TRANSFORM, Analysis of PDEs (math.AP)
101028 Mathematical modelling, X-ray transform of symmetric tensors, Inverse problems for PDEs, Hilbert transform, boundary rigidity problem, Mathematics - Analysis of PDEs, FOS: Mathematics, Boundary rigidity problem, INVERSION-FORMULA, Radon transform, A-analytic maps, RANGE CHARACTERIZATION, SURFACES, Systems of linear first-order PDEs, \(X\)-ray transform of symmetric tensors, DOPPLER TRANSFORM, \(A\)-analytic maps, TENSOR TOMOGRAPHY, attenuated \(X\)-ray transform, 101028 Mathematische Modellierung, Special integral transforms (Legendre, Hilbert, etc.), Attenuated X-ray transform, ATTENUATED RADON-TRANSFORM, Analysis of PDEs (math.AP)
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