Nonuniqueness in inverse Radon problems: The frequency distribution of the ghosts

DOI10.1007/BF01215050zbMath0519.65080OpenAlexW2022981366MaRDI QIDQ1054447

Alfred K. Louis

Publication date: 1984

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173412

zbMATH Keywords

Radon transformeigenvalue problemseries expansionspectrumimage reconstructionghostsreconstruction algorithmsX-ray tomographydominant eigenvaluefrequency distributioncompterized tomographyhigh-frequency componentsinverse Radon problemsnuclear magnetic resonance tomography

Mathematics Subject Classification ID

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)

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Cites Work

• The uncertainty principle in reconstructing functions from projections
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Orthogonal Function Series Expansions and the Null Space of the Radon Transform
• Practical and mathematical aspects of the problem of reconstructing objects from radiographs
• A Sobolev Space Analysis of Picture Reconstruction
• Ghosts in tomography – the null space of the radon transform
• Uniform asymptotic expansions at a caustic
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
• COMPLEX FOURIER--BESSEL TRANSFORMS
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