Inversion of the scalar and vector attenuated X-ray transforms in a unit disc

DOI10.1515/jiip.2007.040zbMath1139.44001OpenAlexW2044040194MaRDI QIDQ5440301

Alexander A. Bukhgeim, Sergeĭ Gavrilovich Kazantsev

Publication date: 4 February 2008

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2007.040

zbMATH Keywords

Radon transformnumerical examplesHilbert transformtransport equationinversion formulaeattenuated X-ray transformfan-beam geometry\(\mathcal A\)-analytic functionsattenuated vectorial X-ray transform

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Numerical methods for integral transforms (65R10) Integral geometry (53C65)

Related Items (12)

On the angular moment operators of attenuated ray transforms of scalar 3D-fields ⋮ The attenuated geodesic x-ray transform ⋮ Efficient tensor tomography in fan-beam coordinates. II: Attenuated transforms ⋮ Inversion formulas and range characterizations for the attenuated geodesic ray transform ⋮ On the range of the \(X\)-ray transform of symmetric tensors compactly supported in the plane ⋮ Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields ⋮ Stability estimates for the local Radon transform ⋮ Generalized attenuated ray transforms and their integral angular moments ⋮ Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces ⋮ A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium ⋮ Partial inversion of the 2D attenuated \(X\)-ray transform with data on an arc ⋮ The semi-analytical method for inversion of a weighted vector ray transform in three dimensions

Cites Work

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• Conditional stability estimates for the two-dimensional problem of restoring the right-hand side and absorption in the transport equation
• Inversion of the attenuated Radon transform
• A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula
• Image reconstruction in 2D SPECT with 180° acquisition
• Stability of the inverse problem for the attenuated Radon transform with 180° data
• The Exponential Radon Transform
• Several results of multidimensional inverse problems theory
• On the range characterization for the two-dimensional attenuated x-ray transformation
• A new approach towards simultaneous activity and attenuation reconstruction in emission tomography
• Numerical solution of the identification problem for the attenuated Radon transform
• On single-photon emission computed tomography imaging based on an exact formula for the nonuniform attenuation correction
• Variable sinograms and redundant information in single-photon emission computed tomography with non-uniform attenuation
• On the attenuated Radon transform with full and partial measurements
• Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
• Fast numerical inversion of the attenuated Radon transform with full and partial measurements

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