Regularizing filtration of projections for two-dimensional tomography algorithms

Συγγραφείς: A. V. Likhachov

Πηγή: Numerical Analysis and Applications. 1:151-162

Θεματικοί όροι: 0301 basic medicine, numerical examples, 0303 health sciences, 03 medical and health sciences, Biomedical imaging and signal processing, regularizing filters, regularizing algorithm, tomography, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations, Radon transform, discrepancy criterion

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/content/pdf/10.1134/S1995423908020067.pdf
https://link.springer.com/article/10.1134/S1995423908020067

On some matrix extrapolation methods

Συγγραφείς: Abderrahim Messaoudi, Khalid Tabaa, Khalide Jbilou

Πηγή: Comptes Rendus. Mathématique. 341:781-786

Θεματικοί όροι: Extrapolation to the limit, deferred corrections, Schur complement, 0101 mathematics, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, matrix extrapolation methods

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2242308
https://doi.org/10.1016/j.crma.2005.10.019
https://www.sciencedirect.com/science/article/pii/S1631073X05004838
https://www.sciencedirect.com/science/article/abs/pii/S1631073X05004838

On local regularization methods for linear Volterra equations and nonlinear equations of Hammerstein type

Συγγραφείς: Zhewei Dai, Patricia K. Lamm

Πηγή: Inverse Problems. 21:1773-1790

Θεματικοί όροι: Other nonlinear integral equations, smoothing operator, numerical examples, sequential Tikhonov regularization, convergence, Volterra integral equations, local regularization method, ill-posed problem, Numerical methods for integral equations, stability, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, future polynomial regularization, convolution kernels, Hammerstein type, nonlinear Volterra integral equation, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://users.math.msu.edu/users/lamm/Preprints/Lamm_Dai_Hammerstein/paper.pdf
https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1773L/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/21/5/016
http://users.math.msu.edu/users/lamm/Preprints/Lamm_Dai_Hammerstein/paper.pdf
https://www.math.msu.edu/~lamm/Preprints/Lamm_Dai_Hammerstein/paper.pdf

On a quasi-optimal regularized projection method for solving operator equations of the first kind

Συγγραφείς: S. G. Solodky

Πηγή: Inverse Problems. 21:1473-1485

Θεματικοί όροι: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Hilbert space, discrepancy principle, ill-posed problem, Showalter method, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Tikhonov method, regularization methods, compact linear operator, Numerical solutions to equations with linear operators, optimal order of accuracy, 0101 mathematics, linear operator equation, regularized projection method algorithm

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2215125
https://doi.org/10.1088/0266-5611/21/4/017
https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1473S/abstract
http://iopscience.iop.org/article/10.1088/0266-5611/21/4/017/pdf

FBP algorithms for attenuated fan-beam projections

Συγγραφείς: Gengsheng L. Zeng, Jiangsheng You, Zhengrong Liang

Πηγή: Inverse Problems. 21:1179-1192

Θεματικοί όροι: Signal theory (characterization, reconstruction, filtering, etc.), fan-beam data reconstruction, 03 medical and health sciences, 0302 clinical medicine, Biomedical imaging and signal processing, fan-beam projections, Biological applications of optics and electromagnetic theory, computed tomography, 0101 mathematics, filtered backprojection reconstruction algorithm, 01 natural sciences, Numerical methods for ill-posed problems for integral equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://europepmc.org/articles/pmc1415202?pdf=render
https://pubmed.ncbi.nlm.nih.gov/16570111
https://ieeexplore.ieee.org/document/1466327/
http://ieeexplore.ieee.org/document/1466327/

Resolution enhancement of spectra using differentiation

Συγγραφείς: Hegland, Markus, Anderssen, Robert S

Πηγή: Inverse Problems. 21:915-934

Θεματικοί όροι: spectroscopy, Statistical methods, Numerical methods for integral equations, 01 natural sciences, Taylor series, modelling spectra, numerical differentiation, 0101 mathematics, Infrared spectroscopy, Integral equations, error analysis, Probability, Other nonlinear integral equations, Problem solving, numerical examples, Keywords: Computational methods, Tikhonov regularization, Spectral lines, nonlinear fitting methods, Numerical methods for ill-posed problems for integral equations, Fourier transforms, Hilbert space framework, Nonlinear fitting method, Error analysis, Mathematical transformations, Estimation, deconvolution problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2190030
https://doi.org/10.1088/0266-5611/21/3/008
https://openresearch-repository.anu.edu.au/handle/1885/76026
https://ui.adsabs.harvard.edu/abs/2005InvPr..21..915H/abstract
https://digitalcollections.anu.edu.au/handle/1885/76026
https://iopscience.iop.org/article/10.1088/0266-5611/21/3/008

On deconvolution problems: numerical aspects

Συγγραφείς: Ramm, Alexander G., Smirnova, Alexandra B.

Συνεισφορές: ramm

Πηγή: Journal of Computational and Applied Mathematics. 176:445-460

Θεματικοί όροι: algorithm, Volterra integral equations, 45D05, 45L05, 45P05, Applied Mathematics, compact operator, Deconvolution, Numerical Analysis (math.NA), Numerical methods for integral equations, deconvolution, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, noisy data, regularization, Volterra equations, Computational Mathematics, Linear ill-posed problems, 0103 physical sciences, FOS: Mathematics, linear ill-posed problems, Mathematics - Numerical Analysis, 0101 mathematics

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/math/0408195
https://zbmath.org/2136532
https://doi.org/10.1016/j.cam.2004.08.001
https://ui.adsabs.harvard.edu/abs/2005JCoAM.176..445R/abstract
https://dl.acm.org/citation.cfm?id=1716615
https://www.sciencedirect.com/science/article/abs/pii/S0377042704003498
https://www.sciencedirect.com/science/article/pii/S0377042704003498
https://core.ac.uk/display/82391326

Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems

Συγγραφείς: Ya-xiang Yuan, Yanfei Wang

Πηγή: Inverse Problems. 21:821-838

Θεματικοί όροι: Other nonlinear integral equations, Hilbert spaces, Numerical optimization and variational techniques, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical solutions to equations with nonlinear operators, stopping rule, Nonlinear ill-posed problems, inverse gravimetry, nonlinear ill-posed problems, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Regularization, trust region method, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://iopscience.iop.org/article/10.1088/0266-5611/21/3/003/pdf
https://iopscience.iop.org/article/10.1088/0266-5611/21/3/003/meta
http://sourcedb.igg.cas.cn/cn/zjrck/200907/W020100601586135546716.pdf
https://iopscience.iop.org/article/10.1088/0266-5611/21/3/003/pdf
http://ui.adsabs.harvard.edu/abs/2005InvPr..21..821W/abstract

Two approaches to the problem of defect correction in vector field tomography solving boundary value problems

Συγγραφείς: Alfred K. Louis, Thomas Schuster, E. Yu. Derevtsov

Πηγή: Journal of Inverse and Ill-Posed Problems. 12:597-626

Θεματικοί όροι: Finite difference methods for boundary value problems involving PDEs, Inverse problems for PDEs, ray transform, Numerical methods for inverse problems for boundary value problems involving PDEs, Neumann problem, Boundary element methods for boundary value problems involving PDEs, Inverse problems in geophysics, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, boundary element method, Boundary value problems for second-order elliptic equations, vector field tomography, inverse problem, 0101 mathematics, Numerical methods for inverse problems for integral equations, Numerical methods for integral transforms, finite difference method, Radon transform, Dirichlet problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2182349
https://doi.org/10.1515/1569394042545111
https://www.degruyter.com/view/j/jiip.2004.12.issue-6/1569394042545111/1569394042545111.xml

Regularization of Mellin-type inverse problems with an application to oil engineering

Συγγραφείς: Olaf Hansen, Silva Fischer, Ronny Ramlau

Πηγή: Linear Algebra and its Applications. 391:125-147

Θεματικοί όροι: Integral operators, Numerical Analysis, convergence, Algebra and Number Theory, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, integral operators, Tikhonov regularization, Mellin convolution operator, Hilbert space, numerical results, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, capillary pressure operator, Linear ill-posed problems, Numerical solutions to equations with linear operators, Morozov's discrepancy principle, linear ill-posed problems, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, Mellin transform

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2117838
https://doi.org/10.1016/j.laa.2004.03.038
https://www.sciencedirect.com/science/article/pii/S0024379504001867
https://www.sciencedirect.com/science/article/abs/pii/S0024379504001867
https://core.ac.uk/display/82190247

Comparing different types of approximators for choosing the parameters in the regularization of ill-posed problems

Συγγραφείς: B. S. Bertram, J. W. Hilgers

Πηγή: Computers & Mathematics with Applications. 48:1779-1790

Θεματικοί όροι: numerical examples, parameter choice, Parameter choice, Fredholm integral equations, Numerical methods for integral equations, Ill-posed problems, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, ill-posed problems, regularization, Computational Mathematics, integral equation, Computational Theory and Mathematics, Modelling and Simulation, Regularization, 0103 physical sciences, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://core.ac.uk/display/82619167
https://www.sciencedirect.com/science/article/pii/S0898122104004274

On the numerical inversion of the Laplace transform of certain holomorphic mappings

Συγγραφείς: LOPEZ FERNANDEZ, MARIA, C, Palencia

Πηγή: Applied Numerical Mathematics. 51:289-303

Θεματικοί όροι: numerical examples, Laplace transform, sinc method, evolutionary equation with memory, numerical inversion, quadrature formula, parallelizable algorithm, 0101 mathematics, 01 natural sciences, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://core.ac.uk/display/54526600
https://www.sciencedirect.com/science/article/abs/pii/S0168927404001059
http://www.sciencedirect.com/science/article/pii/S0168927404001059
https://dl.acm.org/doi/10.1016/j.apnum.2004.06.015
https://hdl.handle.net/11573/844049

High-resolution exponential analysis via regularized numerical inversion of Laplace transforms

Συγγραφείς: V. V. Kryzhniy

Πηγή: Journal of Computational Physics. 199:618-630

Θεματικοί όροι: numerical examples, Laplace transform, Regularization, inverse Laplace transformation, Exponential analysis, 0101 mathematics, Numerical inversion, 01 natural sciences, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2107339
https://doi.org/10.1016/j.jcp.2004.02.017
https://dl.acm.org/doi/10.1016/j.jcp.2004.02.017
https://ui.adsabs.harvard.edu/abs/2004JCoPh.199..618K/abstract
https://www.sciencedirect.com/science/article/pii/S0021999104000981

A finite dimensional realization of the mollifier method for compact operator equations

Συγγραφείς: Shine Lal, M. T. Nair

Πηγή: Mathematics of Computation. 74:1281-1291

Θεματικοί όροι: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Fredholm integral equation, Hilbert space, mollifier method, Fredholm integral equations, Numerical methods for integral equations, Moore-Penrose generalized inverse, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Numerical solutions to equations with linear operators, ill-posed equation, 0101 mathematics, compact operators

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/mcom/2005-74-251/S0025-5718-04-01707-7/S0025-5718-04-01707-7.pdf
https://zbmath.org/2161911
https://doi.org/10.1090/s0025-5718-04-01707-7
https://www.ams.org/mcom/2005-74-251/S0025-5718-04-01707-7/S0025-5718-04-01707-7.pdf
https://ui.adsabs.harvard.edu/abs/2005MaCom..74.1281N/abstract
https://www.ams.org/journals/mcom/2005-74-251/S0025-5718-04-01707-7/home.html
http://dblp.uni-trier.de/db/journals/moc/moc74.html#NairL05
https://dblp.uni-trier.de/db/journals/moc/moc74.html#NairL05

On regularization method for numerical inversion of Laplace transforms

Συγγραφείς: V. V. Kryzhniy

Πηγή: Journal of Inverse and Ill-Posed Problems. 12:279-296

Θεματικοί όροι: numerical examples, convergence, Laplace transform, numerical inversion, stability, 0101 mathematics, 01 natural sciences, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2114291
https://doi.org/10.1515/1569394042215874
https://www.degruyter.com/view/j/jiip.2004.12.issue-3/1569394042215874/1569394042215874.xml

The approximate inverse in action III: 3D-Doppler tomography: The approximate inverse in action. III: 3D-Doppler tomography

Συγγραφείς: Rieder, A., Schuster, Th.

Πηγή: Numerische Mathematik, 97 (2), 353-378

Θεματικοί όροι: ddc:510, 3D-Doppler transform, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Biomedical imaging and signal processing, Linear operators and ill-posed problems, regularization, reconstruction algorithm, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Numerical solutions to equations with linear operators, 3D-Doppler tomography, filtered back projection, 0101 mathematics, Mathematics, Numerical methods for integral transforms, Equations and inequalities involving linear operators, with vector unknowns, Radon transform

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://publikationen.bibliothek.kit.edu/1000011043/762681
https://publikationen.bibliothek.kit.edu/1000011043/762681
https://publikationen.bibliothek.kit.edu/1000011043
https://doi.org/10.5445/IR/1000011043
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-110431

Stability estimates in inverse scattering

Συγγραφείς: Alexander G. Ramm

Πηγή: Lecture Notes in Physics ISBN: 9783662139714
Lecture Notes in Physics ISBN: 9783540575764

Θεματικοί όροι: Inverse problems for PDEs, algorithm, 35R30, 81F15, 73D25, noisy discrete fixed energy data, FOS: Physical sciences, Mathematical Physics (math-ph), Numerical Analysis (math.NA), 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Mathematics - Analysis of PDEs, Scattering theory for PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Mathematical Physics, Diffraction, scattering, Analysis of PDEs (math.AP)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://www.math.ksu.edu/~ramm/papers/285.pdf
http://arxiv.org/abs/math-ph/9911039
https://zbmath.org/95379
https://rd.springer.com/chapter/10.1007/978-3-662-13969-1_28
https://link.springer.com/article/10.1007/BF00047029
https://ui.adsabs.harvard.edu/abs/1999math.ph..11039R/abstract
https://link.springer.com/content/pdf/10.1007/BF00047029.pdf

On the solution of a class of Volterra integral equations of the first kind

Συγγραφείς: FAGNANI, FABIO, PANDOLFI, LUCIANO

Πηγή: Journal of Inverse and Ill-posed Problems. 11:485-503

Θεματικοί όροι: convergence, Volterra integral equations, Lavrientev method, Volterra integral equation, first kind, iterative solution, Numerical methods for integral equations, 0101 mathematics, 01 natural sciences, Numerical methods for ill-posed problems for integral equations

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2069794
https://doi.org/10.1515/156939403770888237
https://iris.polito.it/handle/11583/1399863
https://core.ac.uk/display/11370886
https://hdl.handle.net/11583/1399863

Newton s method for inverse obstacle scattering meets the method of least squares: Newton's method for inverse obstacle scattering meets the method of least squares

Συγγραφείς: Kress, Rainer

Συνεισφορές: Kress, Rainer

Πηγή: Inverse Problems. 19:S91-S104

Θεματικοί όροι: inverse scattering problems, Numerical solutions of ill-posed problems in abstract spaces, regularization, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Numerical methods for inverse problems for boundary value problems involving PDEs, Numerical solutions to equations with nonlinear operators, 4. Education, Numerical methods in optics, Nonlinear ill-posed problems, nonlinear ill-posed problems, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, numerical example, Newton's method, integral equation, Scattering theory for PDEs, inverse obstacle scattering, Inverse problems (including inverse scattering) in optics and electromagnetic theory, Helmholtz equation, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://iopscience.iop.org/article/10.1088/0266-5611/19/6/056
http://ui.adsabs.harvard.edu/abs/2003InvPr..19S..91K/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/19/6/056/pdf
https://resolver.sub.uni-goettingen.de/purl?gro-2/44861

Filter design in three-dimensional cone beam tomography: circular scanning geometry: Filter design in three-dimensional cone beam tomography: Circular scanning geometry

Συγγραφείς: Alfred K. Louis

Πηγή: Inverse Problems. 19:S31-S40

Θεματικοί όροι: regularization, method of approximate inverse, 0202 electrical engineering, electronic engineering, information engineering, linear ill-posed problems, 02 engineering and technology, cone beam tomography, 0101 mathematics, numerical experiments, 01 natural sciences, Numerical methods for integral transforms, Numerical methods for ill-posed problems for integral equations, Radon transform

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://iopscience.iop.org/article/10.1088/0266-5611/19/6/052/pdf
https://iopscience.iop.org/article/10.1088/0266-5611/19/6/052/pdf
http://ui.adsabs.harvard.edu/abs/2003InvPr..19S..31L/abstract