The Radon Transform over Cones with Vertices on the Sphere and Orthogonal Axes

DOI10.1137/16M1079476zbMath1371.44001arXiv1606.03486MaRDI QIDQ5348491

Daniela Schiefeneder, Markus Haltmeier

Publication date: 18 August 2017

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.03486

zbMATH Keywords

numerical resultscomputed tomographyRadon transformseries expansionconical Radon transforminversion methodgeneralized Abel integral equationsuniqueness of reconstructionspherical harmonics decompositionCompton camerasfirst kind Volterra integral equations with zeros in diagonal

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Numerical methods for integral transforms (65R10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Volterra integral equations (45D05)

Related Items (13)

Compton camera imaging and the cone transform: a brief overview ⋮ Inversion of weighted divergent beam and cone transforms ⋮ The conical Radon transform with vertices on triple line segments ⋮ The V-line transform with some generalizations and cone differentiation ⋮ An inversion formula for the horizontal conical Radon transform ⋮ Variational regularization of the weighted conical Radon transform ⋮ Enhancement of Compton camera images reconstructed by inversion of a conical Radon transform ⋮ Inversion formula for the conical Radon transform arising in a single first semicircle second Compton camera with rotation ⋮ Recovery of singularities for the weighted cone transform appearing in Compton camera imaging ⋮ Artifacts in the inversion of the broken ray transform in the plane ⋮ Sampling for the V-line transform with vertex on a circle ⋮ On a three-dimensional Compton scattering tomography system with fixed source ⋮ Analytic Inversion of a Conical Radon Transform Arising in Application of Compton Cameras on the Cylinder

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