Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces

DOI10.1137/15M1016412MaRDI QIDQ2796503

François Monard

Publication date: 29 March 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.07190

zbMATH Keywords

inverse problemscomputerized tomographyDoppler tomographyattenuated X-ray transformsimple surfaces

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Radon transform (44A12) Applications of PDEs on manifolds (58J90) Boundary value problems on manifolds (58J32) Fredholm integral equations (45B05) Geodesic flows in symplectic geometry and contact geometry (53D25) Integral equations with kernels of Cauchy type (45E05)

Related Items (16)

On the angular moment operators of attenuated ray transforms of scalar 3D-fields ⋮ Efficient tensor tomography in Fan-beam coordinates ⋮ Reconstruction formulas for X-ray transforms in negative curvature ⋮ The attenuated geodesic x-ray transform ⋮ Efficient tensor tomography in fan-beam coordinates. II: Attenuated transforms ⋮ The geodesic X-ray transform with a \(\mathrm{GL}(n,\mathbb{C})\)-connection ⋮ Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields ⋮ Sampling the X-ray Transform on Simple Surfaces ⋮ Inversion formulas and range characterizations for the attenuated geodesic ray transform ⋮ Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields ⋮ Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature ⋮ Generalized attenuated ray transforms and their integral angular moments ⋮ The attenuated geodesic ray transform on tensors: generic injectivity and stability ⋮ Coherent Quantum Tomography ⋮ On solenoidal-injective and injective ray transforms of tensor fields on surfaces ⋮ Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations

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