Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds

DOI10.1017/S0305004118000543zbMath1440.53082arXiv1702.07622OpenAlexW2611719098WikidataQ109346780 ScholiaQ109346780MaRDI QIDQ5207970

Mikko Salo, Jere Lehtonen, Joonas Ilmavirta

Publication date: 14 January 2020

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.07622

zbMATH Keywords

tangent functionregular simplexpiecewise constant functionregular tilinggeodesic X-ray transformcompact nontrapping Riemannian manifoldstrictly convex foliationtangent cone of a regular simplextangent space of a regular simplex

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Medical applications (general) (92C50) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Radon transform (44A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Geodesics in global differential geometry (53C22) Integral geometry (53C65) Foliations in differential topology; geometric theory (57R30) Classifying spaces for foliations; Gelfand-Fuks cohomology (57R32)

Related Items (4)

Geodesic ray transform with matrix weights for piecewise constant functions ⋮ Reconstruction of piecewise constant functions from x-ray data ⋮ On solenoidal-injective and injective ray transforms of tensor fields on surfaces ⋮ Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners

Cites Work

• Tensor tomography on surfaces
• Tensor tomography: progress and challenges
• A support theorem for the geodesic ray transform on functions
• The Radon transform.
• Boundary control of PDEs via curvature flows: the view from the boundary. II.
• The inverse problem for the local geodesic ray transform
• Inverse problems: seeing the unseen
• The geodesic X-ray transform with matrix weights
• On manifolds with corners

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