Generalized and attenuated radon transforms: restorative approach to the numerical inversion

DOI10.1088/0266-5611/8/5/008zbMath0760.65117OpenAlexW2034933793MaRDI QIDQ4022039

Leonid A. Kunyansky

Publication date: 17 January 1993

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/8/5/008

zbMATH Keywords

numerical inversiontomographynorm estimateimage restorationattenuated Radon transformgeneralized Radon transformsattenuation correctioniterative restoration algorithms

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12) Numerical methods for integral transforms (65R10) Numerical methods for ill-posed problems for integral equations (65R30)

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Inversion of weighted Radon transforms via finite Fourier series weight approximations ⋮ An example of non-uniqueness for the weighted Radon transforms along hyperplanes in multidimensions ⋮ C-library \texttt{raft}: reconstruction algorithms for tomography. Applications to X-ray fluorescence tomography ⋮ An example of non-uniqueness for Radon transforms with continuous positive rotation invariant weights ⋮ Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces ⋮ A geometric based preprocessing for weighted ray transforms with applications in SPECT ⋮ Coherent Quantum Tomography ⋮ Local tomography with nonsmooth attenuation

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