A geometric based preprocessing for weighted ray transforms with applications in SPECT

DOI10.1515/jiip-2020-0015zbMath1480.44003arXiv1911.05470OpenAlexW3024987707MaRDI QIDQ2042425

F. O. Goncharov

Publication date: 20 July 2021

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.05470

zbMATH Keywords

weighted Radon transformemission tomographyweighted ray transform

Mathematics Subject Classification ID

Radon transform (44A12) Numerical methods for integral transforms (65R10)

Uses Software

• NFFT
• NFFT3

Cites Work

• L\({}^ p\) harmonic analysis and Radon transforms on the Heisenberg group
• The X-ray transform for a generic family of curves and weights
• The invertibility of rotation invariant Radon transforms
• The Radon transform.
• An inversion formula for the attenuated \(X\)-ray transformation
• Integral geometry for tensor fields. Transl. from the Russian
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• A duality for symmetric spaces with applications to group representations
• Inversion of the attenuated Radon transform
• A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula
• On Radon transforms on compact Lie groups
• Combined source and attenuation reconstructions in SPECT
• Local non-injectivity for weighted radon transforms
• Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
• Spherical Functions on a Semisimple Lie Group, I
• Inversion of weighted Radon transforms via finite Fourier series weight approximations
• The inversion problem and applications of the generalized radon transform
• The Dependence of the Generalized Radon Transform on Defining Measures
• Radon Inversion--Variations on a Theme
• Generalized and attenuated radon transforms: restorative approach to the numerical inversion
• An iterative inversion of weighted Radon transforms along hyperplanes
• Microlocal analysis of imaging operators for effective common offset seismic reconstruction
• On single-photon emission computed tomography imaging based on an exact formula for the nonuniform attenuation correction
• Geodesic ray transform with matrix weights for piecewise constant functions
• Weighted Radon transforms for which Chang's approximate inversion formula is exact
• The geodesic X-ray transform with matrix weights
• On Wiener-type filters in SPECT
• Radon-Fourier transforms on symmetric spaces and related group representations
• The Radon Transform and Medical Imaging
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