Inversion ofk-Plane Transforms and Applications in Computer Tomog

DOI10.1137/1031051zbMath0684.44003OpenAlexW2014590864MaRDI QIDQ4734276

Fritz Keinert

Publication date: 1989

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1031051

zbMATH Keywords

Radon transformmedical imagingimage reconstructionpseudodifferential operatorstability estimateslocal reconstructionlocal tomographyInversion formulasdivergent beam transformx-ray transformdivergent k-plane transformparallel beam transformparallel k-plane transformx-ray computer tomography

Mathematics Subject Classification ID

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

Related Items (13)

Reconstruction of functions from their integrals over \(k\)-planes ⋮ Higher-rank wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices ⋮ Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds ⋮ The \(k\)-plane transform on the Heisenberg group ⋮ Norm estimates for \(k\)-plane transforms and geometric inequalities ⋮ Higher-rank Radon transforms on constant curvature spaces ⋮ Curvatures of surfaces and their shadows ⋮ Inversion of exponential \(k\)-plane transforms ⋮ Relaxation factor optimization for common iterative algorithms in optical computed tomography ⋮ Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces ⋮ Inversion of \(k\)-plane transforms via continuous wavelet transforms ⋮ The Calderón reproducing formula, windowed \(X\)-ray transforms, and Radon transforms in \(L^p\)-spaces ⋮ Convolution-backprojection method for the \(k\)-plane transform, and Calderón's identity for ridgelet transforms

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