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Radon series on computational and applied mathematics.
Large scale inverse problems: computational methods and applications in the earth sciences / edited by Mike Cullen, Melina A. Freitag, Stefan Kindermann, Robert Scheichl. — 1 online resource (ix, 203 pages) : illustrations. — (Radon Series on Computational and Applied Mathematics). — EbpS Open Access. — English. — <URL:http://elib.fa.ru/ebsco/641761.pdf>.

Дата создания записи: 21.09.2013

Тематика: Inverse problems (Differential equations); Applied mathematics.; MATHEMATICS — Calculus.; MATHEMATICS — Mathematical Analysis.; Inverse problems (Differential equations)

Коллекции: EBSCO

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Аннотация

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.

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Оглавление

  • 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 assimilation
    • 3 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 equations
      • 2.3 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 imaging
    • 3 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 regularization
    • 1 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

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