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Large scale inverse problems: computational methods and applications in the earth sciences Radon series on computational and applied mathematics./ edited by Mike Cullen, Melina A. Freitag, Stefan Kindermann, Robert Scheichl.
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| dc.contributor.author | Cullen Michael J. P., | |
| dc.contributor.author | Freitag Melina A., | |
| dc.contributor.author | Kindermann Stefan | |
| dc.contributor.author | Scheichl Robert | |
| dc.date.accessioned | 2024-01-29T21:50:05Z | |
| dc.date.available | 2024-01-29T21:50:05Z | |
| dc.date.issued | 2013 | |
| dc.identifier.citation | Large scale inverse problems: computational methods and applications in the earth sciences Radon series on computational and applied mathematics. - 1 online resource (ix, 203 pages) : - URL: https://libweb.kpfu.ru/ebsco/pdf/641761.pdf | |
| dc.identifier.isbn | 9783110282269 | |
| dc.identifier.isbn | 3110282267 | |
| dc.identifier.isbn | 3110282224 | |
| dc.identifier.isbn | 9783110282221 | |
| dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/179967 | |
| dc.description | EbpS Open Access | |
| dc.description | English. | |
| dc.description | Includes bibliographical references. | |
| dc.description.abstract | This book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. | |
| dc.description.tableofcontents | Preface; Synergy of inverse problems and data assimilation techniques; 1 Introduction; 2 Regularization theory; 3 Cycling, Tikhonov regularization and 3DVar; 4 Error analysis; 5 Bayesian approach to inverse problems; 6 4DVar; 7 Kalman filter and Kalman smoother; 8 Ensemble methods; 9 Numerical examples; 9.1 Data assimilation for an advection-diffusion system; 9.2 Data assimilation for the Lorenz-95 system; 10 Concluding remarks; Variational data assimilation for very large environmental problems; 1 Introduction; 2 Theory of variational data assimilation. | |
| dc.description.tableofcontents | 2.1 Incremental variational data assimilation3 Practical implementation; 3.1 Model development; 3.2 Background error covariances; 3.3 Observation errors; 3.4 Optimization methods; 3.5 Reduced order approaches; 3.6 Issues for nested models; 3.7 Weak-constraint variational assimilation; 4 Summary and future perspectives; Ensemble filter techniques for intermittent data assimilation; 1 Bayesian statistics; 1.1 Preliminaries; 1.2 Bayesian inference; 1.3 Coupling of random variables; 1.4 Monte Carlo methods; 2 Stochastic processes; 2.1 Discrete time Markov processes. | |
| dc.description.tableofcontents | 2.2 Stochastic difference and differential equations2.3 Ensemble prediction and sampling methods; 3 Data assimilation and filtering; 3.1 Preliminaries; 3.2 SequentialMonte Carlo method; 3.3 Ensemble Kalman filter (EnKF); 3.4 Ensemble transform Kalman-Bucy filter; 3.5 Guided sequential Monte Carlo methods; 3.6 Continuous ensemble transform filter formulations; 4 Concluding remarks; Inverse problems in imaging; 1 Mathematicalmodels for images; 2 Examples of imaging devices; 2.1 Optical imaging; 2.2 Transmission tomography; 2.3 Emission tomography; 2.4 MR imaging; 2.5 Acoustic imaging. | |
| dc.description.tableofcontents | 2.6 Electromagnetic imaging3 Basic image reconstruction; 3.1 Deblurring and point spread functions; 3.2 Noise; 3.3 Reconstruction methods; 4 Missing data and prior information; 4.1 Prior information; 4.2 Undersampling and superresolution; 4.3 Inpainting; 4.4 Surface imaging; 5 Calibration problems; 5.1 Blind deconvolution; 5.2 Nonlinear MR imaging; 5.3 Attenuation correction in SPECT; 5.4 Blind spectral unmixing; 6 Model-based dynamic imaging; 6.1 Kinetic models; 6.2 Parameter identification; 6.3 Basis pursuit; 6.4 Motion and deformation models; 6.5 Advanced PDE models. | |
| dc.description.tableofcontents | The lost honor of l2-based regularization1 Introduction; 2 l1-based regularization; 3 Poor data; 4 Large, highly ill-conditioned problems; 4.1 Inverse potential problem; 4.2 The effect of ill-conditioning on L1 regularization; 4.3 Nonlinear, highly ill-posed examples; 5 Summary; List of contributors. | |
| dc.language | English | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Radon Series on Computational and Applied Mathematics | |
| dc.relation.ispartofseries | Radon series on computational and applied mathematics. | |
| dc.subject.other | Inverse problems (Differential equations) | |
| dc.subject.other | Applied mathematics. | |
| dc.subject.other | MATHEMATICS -- Calculus. | |
| dc.subject.other | MATHEMATICS -- Mathematical Analysis. | |
| dc.subject.other | Inverse problems (Differential equations) | |
| dc.subject.other | Electronic books. | |
| dc.subject.other | Electronic books. | |
| dc.title | Large scale inverse problems: computational methods and applications in the earth sciences Radon series on computational and applied mathematics./ edited by Mike Cullen, Melina A. Freitag, Stefan Kindermann, Robert Scheichl. | |
| dc.type | Book | |
| dc.description.pages | 1 online resource (ix, 203 pages) : | |
| dc.collection | Электронно-библиотечные системы | |
| dc.source.id | EN05CEBSCO05C103063 |
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