Large scale inverse problems: computational methods and applications in the earth sciences
Saved in:
| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
<<de>> Gruyter
2013
|
| Series: | Radon series on computational and applied mathematics
13 |
| Subjects: | |
| Online Access: | Volltext Inhaltsverzeichnis |
| Item Description: | Erscheint auch als Open Access bei De Gruyter |
| Physical Description: | IX, 203 S. Ill., graph. Darst. |
| ISBN: | 9783110282221 |
| DOI: | 10.1515/9783110282269 |
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CONTENTS
PREFACE* V
MELINAA. FREITAGAND ROLAND W. E. POTTHAST
SYNERGY OF INVERSE PROBLEMS
AND DATA ASSIMILATION TECHNIQUES 1
1
INTRODUCTION 2
2
REGULARIZATION THEORY 6
3
CYCLING, TIKHONOV REGULARIZATION AND 3DVAR 8
4
X
ERROR ANALYSIS 12
5
BAYESIAN APPROACH TO INVERSE PROBLEMS 14
6
4DVAR 19
7
KALMAN FILTER AND KALMAN SMOOTHER 23
8
ENSEMBLE METHODS 29
9
NUMERICAL EXAMPLES 34
9.1
DATA ASSIMILATION FOR AN ADVECTION-DIFFUSION SYSTEM 34
9.2
DATA ASSIMILATION FOR THE LORENZ-95 SYSTEM 41
10
CONCLUDING REMARKS 48
AMOS S. LAWLESS
VARIATIONAL DATA ASSIMILATION FOR VERY LARGE
ENVIRONMENTAL PROBLEMS
1
INTRODUCTION 55
2
THEORY OF VARIATIONAL DATA ASSIMILATION 56
2.1
INCREMENTAL VARIATIONAL DATA ASSIMILATION 60
3
PRACTICAL IMPLEMENTATION 62
3.1
MODEL DEVELOPMENT 62
3.2
BACKGROUND ERROR COVARIANCES 64
3.3
OBSERVATION ERRORS 70
3.4
OPTIMIZATION METHODS 73
3.5
REDUCED ORDER APPROACHES 75
3.6
ISSUES FOR NESTED MODELS 79
3.7
WEAK-CONSTRAINT VARIATIONAL ASSIMILATION 81
4
SUMMARY AND FUTURE PERSPECTIVES 83
SEBASTIAN REICH AND
COLIN
J. COTTER
ENSEMBLE FILTER TECHNIQUES FOR INTERMITTENT
DATA ASSIMILATION 91
1 BAYESIAN STATISTICS 91
1.1 PRELIMINARIES 92
1.2 BAYESIAN INFERENCE 95
1.3 COUPLING OF RANDOM VARIABLES 98
1.4 MONTE CARLO METHODS 104
HTTP://D-NB.INFO/1030086168
VIII
CONTENTS
2 STOCHASTIC PROCESSES 106
2.1 DISCRETE TIME MARKOV PROCESSES 107
2.2 STOCHASTIC DIFFERENCE AND DIFFERENTIAL EQUATIONS 108
2.3 ENSEMBLE PREDICTION AND SAMPLING METHODS 112
3 DATA ASSIMILATION AND FILTERING 115
3.1 PRELIMINARIES 115
3.2 SEQUENTIAL MONTE CARLO METHOD 116
3.3 ENSEMBLE KALMAN FILTER (ENKF) 119
3.4 ENSEMBLE TRANSFORM KALMAN-BUCY FILTER 122
3.5 GUIDED SEQUENTIAL MONTE CARLO METHODS 126
3.6 CONTINUOUS ENSEMBLE TRANSFORM FILTER FORMULATIONS 127
4 CONCLUDING REMARKS 132
MARTIN BURGER,
HENDRIK DIRKS AND JAHN
MIILLER
INVERSE PROBLEMS
IN IMAGING 135
1 MATHEMATICAL MODELS FOR IMAGES 136
2 EXAMPLES OF IMAGING DEVICES 139
2.1 OPTICAL IMAGING 139
2.2 TRANSMISSION TOMOGRAPHY 139
2.3 EMISSION TOMOGRAPHY 141
2.4 MR IMAGING 143
2.5 ACOUSTIC IMAGING 143
2.6 ELECTROMAGNETIC IMAGING 144
3 BASIC IMAGE RECONSTRUCTION 144
3.1 DEBLURRING AND POINT SPREAD FUNCTIONS 145
3.2 NOISE 146
3.3 RECONSTRUCTION METHODS.?* 147
4 MISSING DATA AND PRIOR INFORMATION 149
4.1 PRIOR INFORMATION 149
4.2 UNDERSAMPLINGAND SUPERRESOLUTION 152
4.3 INPAINTING 155
4.4 SURFACE IMAGING 158
5 CALIBRATION PROBLEMS 161
5.1 BLIND DECONVOLUTION 162
5.2 NONLINEAR MR IMAGING 163
5.3 ATTENUATION CORRECTION IN SPECT 163
5.4 BLIND SPECTRAL UNMIXING 164
6 MODEL-BASED DYNAMIC IMAGING 165
6.1 KINETIC MODELS 166
6.2 PARAMETER IDENTIFICATION 168
6.3 BASIS PURSUIT 170
CONTENTS
* IX
6.4 MOTION AND DEFORMATION MODELS 172
6.5 ADVANCED PDE MODELS 174
KEESVANDEN DOEL, URI
M.ASCHERAND ELDAD HABER
THE LOST HONOR OF ^2-BASED REGULARIZATION 181
1 INTRODUCTION 181
2 ^-BASED REGULARIZATION 185
3 POOR DATA 188
4 LARGE, HIGHLY ILL-CONDITIONED PROBLEMS 191
4.1 INVERSE POTENTIAL PROBLEM 191
4.2 THE EFFECT OF ILL-CONDITIONING ON LI REGULARIZATION 194
4.3 NONLINEAR, HIGHLY ILL-POSED EXAMPLES 198
5 SUMMARY 200
LIST OF CONTRIBUTORS 204 |
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| physical | IX, 203 S. Ill., graph. Darst. |
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| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | Radon series on computational and applied mathematics |
| series2 | Radon series on computational and applied mathematics |
| spellingShingle | Large scale inverse problems computational methods and applications in the earth sciences Radon series on computational and applied mathematics Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)1071861417 |
| title | Large scale inverse problems computational methods and applications in the earth sciences |
| title_auth | Large scale inverse problems computational methods and applications in the earth sciences |
| title_exact_search | Large scale inverse problems computational methods and applications in the earth sciences |
| title_full | Large scale inverse problems computational methods and applications in the earth sciences ed. by Mike Cullen ... |
| title_fullStr | Large scale inverse problems computational methods and applications in the earth sciences ed. by Mike Cullen ... |
| title_full_unstemmed | Large scale inverse problems computational methods and applications in the earth sciences ed. by Mike Cullen ... |
| title_short | Large scale inverse problems |
| title_sort | large scale inverse problems computational methods and applications in the earth sciences |
| title_sub | computational methods and applications in the earth sciences |
| topic | Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Inverses Problem Konferenzschrift 2011 Linz |
| url | https://doi.org/10.1515/9783110282269 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026918266&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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