Optimal Regularized Reconstruction in Computerized Tomography

DOI10.1137/0908076zbMath0638.65094OpenAlexW2005597743MaRDI QIDQ3779709

Didier A. Girard

Publication date: 1987

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0908076

zbMATH Keywords

comparison of methodsRadon transformTikhonov-Phillips regularizationcomputerized tomographycross-validationdiscrepancy principleill-posed problemimage reconstructionfiltered backprojection algorithmoptimal regularization parameterreconstruction spacestochastic model for the noise in the datatime-of-flight emissions tomography

Mathematics Subject Classification ID

Medical applications (general) (92C50) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10)

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Multiresolution Parameter Choice Method for Total Variation Regularized Tomography ⋮ A fast ``Monte-Carlo cross-validation procedure for large least squares problems with noisy data ⋮ Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise. ⋮ On the choice of high-dimensional regression parameters in Gaussian random tomography ⋮ Variational trivariate fitting using Worsey-Piper macro elements on tetrahedral partitions ⋮ Asymptotic comparison of (partial) cross-validation, GCV and randomized GCV in nonparametric regression ⋮ Simultaneous Sensing Error Recovery and Tomographic Inversion Using an Optimization-Based Approach ⋮ Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography

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