Reconstruction from cone integral transforms

DOI10.1088/1361-6420/aa863ezbMath1382.44001OpenAlexW2750405289MaRDI QIDQ4592681

Victor P. Palamodov

Publication date: 8 November 2017

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/d2b39b2310ded84befbbf597dca2597897127a4e

zbMATH Keywords

Fourier transformconvolutionRadon transforminversion formulareconstruction of imagesCompton cameracone transformnongeodesic Funk transformCompton tomographysingular ray transform

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Radon transform (44A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for integral transforms (65R10)

Related Items (13)

The first 100 years of the Radon transform ⋮ Nonreciprocal broken ray transforms with applications to fluorescence imaging ⋮ Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere ⋮ Recovering a function from its integrals over conical surfaces through relations with the Radon transform ⋮ An SVD in Spherical Surface Wave Tomography ⋮ Compton camera imaging and the cone transform: a brief overview ⋮ Some analytic properties of the cone transform ⋮ The V-line transform with some generalizations and cone differentiation ⋮ Variational regularization of the weighted conical Radon transform ⋮ Enhancement of Compton camera images reconstructed by inversion of a conical Radon transform ⋮ Reconstructions from integrals over non-analytic manifolds ⋮ Orthogonal function series formulae for inversion of the conical Radon transform with a fixed central axis ⋮ Singular value decomposition of the attenuated conical Radon transform with a fixed central axis and opening angle

Cites Work

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• Exact reconstruction formulas for a Radon transform over cones
• Exact inversion of the conical Radon transform with a fixed opening angle
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