ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Large Scale Inverse Problems Computational Methods and Applications in the Earth Sciences

:	Mike Cullen, Melina A Freitag, Stefan Kindermann, Robert Scheichl
:	Large Scale Inverse Problems Computational Methods and Applications in the Earth Sciences
:	Walter de Gruyter GmbH& Co.KG
:	9783110282269
:	Radon Series on Computational and Applied MathematicsISSN
:	1
:	CHF 0.50
:

:	Mathematik
:	English

:	212
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

Mike Cullen, MET Office, Exeter, UK;Melina Freitag, University of Bath, UK;Stefan Kindermann, Johann Kepler University Linz, Austria;Robert Scheichl, University of Bath, UK.

	Preface	5
	Synergy of inverse problems and data assimilation techniques	11
	1 Introduction	12
	2 Regularization theory	16
	3 Cycling, Tikhonov regularization and 3DVar	18
	4 Error analysis	22
	5 Bayesian approach to inverse problems	24
	6 4DVar	29
	7 Kalman filter and Kalman smoother	33
	8 Ensemble methods	39
	9 Numerical examples	44
	9.1 Data assimilation for an advection-diffusion system	44
	9.2 Data assimilation for the Lorenz-95 system	51
	10 Concluding remarks	58
	Variational data assimilation for very large environmental problems	65
	1 Introduction	65
	2 Theory of variational data assimilation	66
	2.1 Incremental variational data assimilation	70
	3 Practical implementation	72
	3.1 Model development	72
	3.2 Background error covariances	74
	3.3 Observation errors	80
	3.4 Optimization methods	83
	3.5 Reduced order approaches	85
	3.6 Issues for nested models	89
	3.7 Weak-constraint variational assimilation	91
	4 Summary and future perspectives	93
	Ensemble filter techniques for intermittent data assimilation	101
	1 Bayesian statistics	101
	1.1 Preliminaries	102
	1.2 Bayesian inference	105
	1.3 Coupling of random variables	108
	1.4 Monte Carlo methods	114
	2 Stochastic processes	116
	2.1 Discrete time Markov processes	117
	2.2 Stochastic difference and differential equations	118
	2.3 Ensemble prediction and sampling methods	122
	3 Data assimilation and filtering	125
	3.1 Preliminaries	125
	3.2 SequentialMonte Carlo method	126
	3.3 Ensemble Kalman filter (EnKF)	129
	3.4 Ensemble transform Kalman–Bucy filter	132
	3.5 Guided sequential Monte Carlo methods	136
	3.6 Continuous ensemble transform filter formulations	137
	4 Concluding remarks	142
	Inverse problems in imaging	145
	1 Mathematicalmodels for images	146
	2 Examples of imaging devices	149
	2.1 Optical imaging	149
	2.2 Transmission tomography	149
	2.3 Emission tomography	151
	2.4 MR imaging	153
	2.5 Acoustic imaging	153
	2.6 Electromagnetic imaging	154
	3 Basic image reconstruction	154
	3.1 Deblurring and point spread functions	155
	3.2 Noise	156
	3.3 Reconstruction methods	157
	4 Missing data and prior information	159
	4.1 Prior information	159
	4.2 Undersampling and superresolution	162
	4.3 Inpainting	165
	4.4 Surface imaging	168
	5 Calibration problems	171
	5.1 Blind deconvolution	172
	5.2 Nonlinear MR imaging	173
	5.3 Attenuation correction in SPECT	173
	5.4 Blind spectral unmixing	174
	6 Model-based dynamic imaging	175
	6.1 Kinetic models	176
	6.2 Parameter identification	178
	6.3 Basis pursuit	180
	6.4 Motion and deformation models	182
	6.5 Advanced PDE models	184
	The lost honor of l2-based regularization	191
	1 Introduction	191
	2 l1-based regularization	195
	3 Poor data	198
	4 Large, highly ill-conditioned problems	201
	4.1 Inverse potential problem	201
	4.2 The effect of ill-conditioning on L1 regularization	204
	4.3 Nonlinear, highly ill-posed examples	208
	5 Summary	210
	List of contributors	214