Inversion of the V-line Radon transform in a disc and its applications in imaging

DOI10.1016/j.camwa.2012.01.059zbMath1252.44003OpenAlexW1988716939MaRDI QIDQ692244

Gaik Ambartsoumian

Publication date: 4 December 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2012.01.059

zbMATH Keywords

inversionRadonbroken-ray transformV-line transform

Mathematics Subject Classification ID

Radon transform (44A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Application of orthogonal and other special functions (94A11)

Related Items (20)

Stability estimate for the broken non-abelian x-ray transform in Minkowski space ⋮ Analytical reconstruction formula for \(n\)-dimensional conical Radon transform ⋮ Nonreciprocal broken ray transforms with applications to fluorescence imaging ⋮ Three-Dimensional Image Reconstruction from Compton Camera Data ⋮ A series formula for inversion of the V-line Radon transform in a disc ⋮ Recovering a function from its integrals over conical surfaces through relations with the Radon transform ⋮ Compton camera imaging and the cone transform: a brief overview ⋮ Inversion of weighted divergent beam and cone transforms ⋮ V-line 2-tensor tomography in the plane ⋮ Some analytic properties of the cone transform ⋮ The V-line transform with some generalizations and cone differentiation ⋮ An inversion formula for the horizontal conical Radon transform ⋮ The broken ray transform on the square ⋮ Inversion and symmetries of the star transform ⋮ Artifacts in the inversion of the broken ray transform in the plane ⋮ On the Determination of a Function from Its Conical Radon Transform with a Fixed Central Axis ⋮ Generalized V-line transforms in 2D vector tomography ⋮ The broken ray transform: additional properties and new inversion formula ⋮ Sampling for the V-line transform with vertex on a circle ⋮ Microlocal Analysis of Generalized Radon Transforms from Scattering Tomography

Cites Work

• Unnamed Item
• Detecting small low emission radiating sources
• Mathematical Methods in Image Reconstruction
• Inversion of the circular Radon transform on an annulus
• On new {\mathfrak V}-line Radon transforms in \mathbb {R}^{2} and their inversion
• Inversion formulas for the broken-ray Radon transform
• Singularities of the X-Ray Transform and Limited Data Tomography in $\mathbb{R}^2 $ and $\mathbb{R}^3 $

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