Analytic Inversion of a Conical Radon Transform Arising in Application of Compton Cameras on the Cylinder

DOI10.1137/16M1083116zbMath1365.65275arXiv1607.00867OpenAlexW2963048996MaRDI QIDQ5266384

Sunghwan Moon, Markus Haltmeier

Publication date: 2 June 2017

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00867

zbMATH Keywords

inversion formulaimage reconstructionconical Radon transformsingle photon emission computed tomographynuclear imagingCompton camerasmechanical collimation

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Radon transform (44A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for integral transforms (65R10)

Related Items (18)

Nonreciprocal broken ray transforms with applications to fluorescence imaging ⋮ Recovering a function from its integrals over conical surfaces through relations with the Radon transform ⋮ Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography ⋮ Compton camera imaging and the cone transform: a brief overview ⋮ Inversion of weighted divergent beam and cone transforms ⋮ Solution of a certain problem of scattering by using of the maximum entropy principle ⋮ 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 ⋮ Singular value decomposition of the attenuated conical Radon transform with a fixed central axis and opening angle ⋮ Injectivity and Range Description of Integral Moment Transforms Over $m$-Tensor Fields in $\mathbb{R}^n$ ⋮ Sampling for the V-line transform with vertex on a circle ⋮ On a three-dimensional Compton scattering tomography system with fixed source ⋮ Microlocal Analysis of Generalized Radon Transforms from Scattering Tomography

Cites Work

• Unnamed Item
• The Radon transform.
• Detecting small low emission radiating sources
• The Mathematics of Computerized Tomography
• On artifacts in limited data spherical Radon transform: curved observation surface
• On the Determination of a Function from Its Conical Radon Transform with a Fixed Central Axis
• Is a Curved Flight Path in SAR Better than a Straight One?
• On new {\mathfrak V}-line Radon transforms in \mathbb {R}^{2} and their inversion
• Exact Inversion of the Cone Transform Arising in an Application of a Compton Camera Consisting of Line Detectors
• Some inversion formulas for the cone transform
• Inversion formulas for cone transforms arising in application of Compton cameras
• Artifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and Sonar
• How strong are streak artifacts in limited angle computed tomography?
• The Radon Transform over Cones with Vertices on the Sphere and Orthogonal Axes
• Exact reconstruction formulas for a Radon transform over cones
• Exact inversion of the conical Radon transform with a fixed opening angle
• Radon transforms on a class of cones with fixed axis direction
• Representation of a Function by Its Line Integrals, with Some Radiological Applications
• The Radon Transform and Medical Imaging

This page was built for publication: Analytic Inversion of a Conical Radon Transform Arising in Application of Compton Cameras on the Cylinder