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Large scale inverse problems : computational methods and applications in the earth sciences /
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 an...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Boston :
De Gruyter,
[2013]
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| Colección: | Radon series on computational and applied mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.