Ghosts in tomography – the null space of the radon transform
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Publication:3909494
DOI10.1002/mma.1670030102zbMath0459.44004OpenAlexW2151223350MaRDI QIDQ3909494
Publication date: 1981
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.1670030102
Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Other natural sciences (mathematical treatment) (92F05) Integral equations with miscellaneous special kernels (45H05)
Related Items (12)
Local algorithms in exterior tomography ⋮ Biorthogonal decompositions of the Radon transform by multivariate interpolation ⋮ The Radon transform with finitely many angles * ⋮ Tomographic inverse problems: mathematical challenges and novel applications. Abstracts from the workshop held April 30 -- May 5, 2023 ⋮ Null spaces and ranges for the classical and spherical Radon transforms ⋮ Microlocal Analysis in Tomography ⋮ Null space and resolution in dynamic computerized tomography ⋮ Nonuniqueness in inverse Radon problems: The frequency distribution of the ghosts ⋮ A new proof of the support theorem and the range characterization for the Radon transform ⋮ Tomographic reconstruction by maximum entropy in the mean: Unconstrained reconstructions ⋮ Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform ⋮ Convexity properties of inverse problems with variational constraints
Cites Work
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- The angles between the null spaces of X rays
- Projections, reconstructions and orthogonal functions
- On the reconstruction of a function on a circular domain from a sampling of its line integrals
- The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
- Practical and mathematical aspects of the problem of reconstructing objects from radiographs
- A Sobolev Space Analysis of Picture Reconstruction
- Picture reconstruction from projections in restricted range
- Uniform asymptotic expansions at a caustic
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