Asymptotic Analysis of the SVD for the Truncated Hilbert Transform with Overlap

DOI10.1137/140952296zbMath1322.65117arXiv1507.01141OpenAlexW2009112895MaRDI QIDQ5253429

Michel Defrise, Rima Alaifari, Alexander Katsevich

Publication date: 26 May 2015

Published in: SIAM Journal on Mathematical Analysis, Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01141

zbMATH Keywords

algorithmstabilityconvergenceinverse problemRadon transformintegral transformerror analysisHilbert transformspectrumcomputerized tomographyasymptotic analysisTikhonov regularizationtomographytruncated singular value decompositionreconstructionill-posednesstruncated Hilbert transformlimited datasingular value decomposition (SVD)back-projection

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Radon transform (44A12) Numerical methods for integral transforms (65R10) Numerical methods for inverse problems for integral equations (65R32) Inverse problems for integral equations (45Q05)

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Lower bounds for the Dyadic Hilbert transform ⋮ ROI reconstruction from truncated cone-beam projections ⋮ Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach ⋮ Diagonalization of the finite Hilbert transform on two adjacent intervals ⋮ Quantitative invertibility and approximation for the truncated Hilbert and Riesz transforms ⋮ On two methods for quantitative unique continuation results for some nonlocal operators ⋮ Spectral analysis and decomposition of normal operators related with the multi-interval finite Hilbert transform ⋮ On the spectral properties of the Hilbert transform operator on multi-intervals ⋮ On Sobolev instability of the interior problem of tomography ⋮ Ill-Posed Problems: From Linear to Nonlinear and Beyond

Cites Work

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• Crofton's function and inversion formulas in real integral geometry
• The Mathematics of Computerized Tomography
• Singular value decomposition for the truncated Hilbert transform: part II
• Singular value decomposition for the truncated Hilbert transform
• Finite Hilbert transform with incomplete data: null-space and singular values
• Indefinite Sturm–Liouville problems
• Spectral Analysis of the Truncated Hilbert Transform with Overlap
• Truncated Hilbert transform and image reconstruction from limited tomographic data

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