Introduction to inverse problems in imaging:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bristol [u.a.]
Inst. of Physics Publ.
1998
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 351 S. Ill., graph. Darst. |
| ISBN: | 0750304391 0750304359 |
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| 100 | 1 | |a Bertero, Mario |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to inverse problems in imaging |c Mario Bertero ; Patricia Boccacci |
| 264 | 1 | |a Bristol [u.a.] |b Inst. of Physics Publ. |c 1998 | |
| 300 | |a XI, 351 S. |b Ill., graph. Darst. | ||
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| 650 | 7 | |a Problèmes inverses (équations différentielle) |2 ram | |
| 650 | 7 | |a Traitement d'images - Mathématiques |2 ram | |
| 650 | 7 | |a déconvolution |2 inriac | |
| 650 | 7 | |a problème inverse |2 inriac | |
| 650 | 7 | |a problème mal posé |2 inriac | |
| 650 | 7 | |a restauration image |2 inriac | |
| 650 | 7 | |a traitement image |2 inriac | |
| 650 | 7 | |a équation différentielle |2 inriac | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Image processing |x Mathematics | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
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Datensatz im Suchindex
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| adam_text | INTRODUCTION TO INVERSE PROBLEMS IN IMAGING MARIO BERTERO DEPARTMENT OF
COMPUTER AND INFORMATION SCIENCES UNIVERSITY OF GENOVA PATRIZIA BOCCACCI
DEPARTMENT OF PHYSICS UNIVERSITY OF GENOVA INSTITUTE OF PHYSICS
PUBLISHING BRISTOL AND PHILADELPHIA CONTENTS PREFACE XI INTRODUCTION 1
1.1 WHAT IS AN INVERSE PROBLEM? 1 1.2 WHAT IS AN ILL-POSED PROBLEM? 5
1.3 HOW TO CURE ILL-POSEDNESS 9 1.4 AN OUTLINE OF THE BOOK 11 PART 1
IMAGE DECONVOLUTION 17 2 SOME MATHEMATICAL TOOLS 19 2.1 THE FOURIER
TRANSFORM (FT) 19 2.2 BANDLIMITED FUNCTIONS AND SAMPLING THEOREMS 22 2.3
CONVOLUTION OPERATORS 27 2.4 THE DISCRETE FOURIER TRANSFORM (DFT) 30 2.5
CYCLIC MATRICES 36 2.6 RELATIONSHIP BETWEEN FT AND DFT 39 2.7
DISCRETIZATION OF THE CONVOLUTION PRODUCT 42 3 EXAMPLES OF IMAGE
BLURRING 50 3.1 BLURRING AND NOISE 50 3.2 LINEAR MOTION BLUR 54 3.3
OUT-OF-FOCUS BLUR 58 3.4 DIFFRACTION-LIMITED IMAGING SYSTEMS 60 3.5
ATMOSPHERIC TURBULENCE BLUR 67 3.6 NEAR-FIELD ACOUSTIC HOLOGRAPHY 69 4
THE ILL-POSEDNESS OF IMAGE DECONVOLUTION 75 4.1 FORMULATION OF THE
PROBLEM 75 4.2 WELL-POSED AND ILL-POSED PROBLEMS 77 4.3 EXISTENCE OF THE
SOLUTION AND INVERSE FILTERING 79 4.4 DISCRETIZATION: FROM ILL-POSEDNESS
TO ILL-CONDITIONING 81 VII VIII CONTENTS 4.5 BANDLIMITED SYSTEMS:
LEAST-SQUARES SOLUTIONS AND GENERALIZED SOLUTION 86 4.6 APPROXIMATE
SOLUTIONS AND THE USE OF A PRIORI INFORMATION 90 4.7 CONSTRAINED
LEAST-SQUARES SOLUTIONS 94 5 REGULARIZATION METHODS 98 5.1 LEAST-SQUARES
SOLUTIONS WITH PRESCRIBED ENERGY 98 5.2 APPROXIMATE SOLUTIONS WITH
MINIMAL ENERGY 104 5.3 REGULARIZATION ALGORITHMS IN THE SENSE OF
TIKHONOV 107 5.4 REGULARIZATION AND FILTERING 113 5.5 THE GLOBAL POINT
SPREAD FUNCTION: RESOLUTION AND GIBBS OSCILLATIONS 119 5.6 CHOICE OF THE
REGULARIZATION PARAMETER 127 6 ITERATIVE REGULARIZATION METHODS 137 6.1
THE VAN CITTERT AND LANDWEBER METHODS 137 6.2 THE PROJECTED LANDWEBER
METHOD 147 6.3 THE PROJECTED LANDWEBER METHOD FOR THE COMPUTATION OF
CONSTRAINED REGULARIZED SOLUTIONS 154 6.4 THE STEEPEST DESCENT AND THE
CONJUGATE GRADIENT METHOD 157 6.5 FILTERING PROPERTIES OF THE CONJUGATE
GRADIENT METHOD 165 7 STATISTICAL METHODS 168 7.1 MAXIMUM LIKELIHOOD
(ML) METHODS 168 7.2 THE ML METHOD IN THE CASE OF GAUSSIAN NOISE 172 7.3
THE ML METHOD IN THE CASE OF POISSON NOISE 175 7.4 BAYESIAN METHODS 183
7.5 THE WIENER FILTER 184 PART 2 LINEAR INVERSE IMAGING PROBLEMS 189
EXAMPLES OF LINEAR INVERSE PROBLEMS 191 8.1 SPACE-VARIANT IMAGING
SYSTEMS 191 8.2 X-RAY TOMOGRAPHY 194 8.3 EMISSION TOMOGRAPHY 200 8.4
INVERSE DIFFRACTION AND INVERSE SOURCE PROBLEMS 206 8.5 LINEARIZED
INVERSE SCATTERING PROBLEMS 214 SINGULAR VALUE DECOMPOSITION (SVD) 220
9.1 MATHEMATICAL DESCRIPTION OF LINEAR IMAGING SYSTEMS 220 9.2 SVD OF A
MATRIX 225 9.3 SVD OF A SEMI-DISCRETE MAPPING 231 9.4 SVD OF AN INTEGRAL
OPERATOR WITH SQUARE-INTEGRABLE KERNEL 234 9.5 SVD OF THE RADON
TRANSFORM 240 CONTENTS IX 10 INVERSION METHODS REVISITED 247 10.1 THE
GENERALIZED SOLUTION 247 10.2 THE TIKHONOV REGULARIZATION METHOD 253
10.3 TRUNCATED SVD - 256 10.4 ITERATIVE REGULARIZATION METHODS 259 10.5
STATISTICAL METHODS 263 11 FOURIER-BASED METHODS FOR SPECIFIC PROBLEMS
268 11.1 THE FOURIER SLICE THEOREM IN TOMOGRAPHY 268 11.2 THE FILTERED
BACKPROJECTION (FBP) METHOD IN TOMOGRAPHY 272 11.3 IMPLEMENTATION OF THE
DISCRETE FBP 277 11.4 RESOLUTION AND SUPER-RESOLUTION IN IMAGE
RESTORATION 280 11.5 OUT-OF-BAND EXTRAPOLATION 284 11.6 THE GERCHBERG
METHOD AND ITS GENERALIZATION 289 12 COMMENTS AND CONCLUDING REMARKS 295
12.1 DOES THERE EXIST A GENERAL-PURPOSE METHOD? 295 12.2 IN PRAISE OF
SIMULATION 302 PART 3 MATHEMATICAL APPENDICES 309 A EUCLIDEAN AND
HILBERT SPACES OF FUNCTIONS 311 B LINEAR OPERATORS IN FUNCTION SPACES
317 C EUCLIDEAN VECTOR SPACES AND MATRICES 322 D PROPERTIES OF THE DFT
AND THE FFT ALGORITHM 328 E MINIMIZATION OF QUADRATIC FUNCTIONALS 335 F
CONTRACTION AND NON-EXPANSIVE MAPPINGS 339 G THE EM METHOD 343
REFERENCES 346 INDEX 347
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| author | Bertero, Mario Boccacci, Patrizia |
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| discipline | Physik Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| language | English |
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| physical | XI, 351 S. Ill., graph. Darst. |
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| spelling | Bertero, Mario Verfasser aut Introduction to inverse problems in imaging Mario Bertero ; Patricia Boccacci Bristol [u.a.] Inst. of Physics Publ. 1998 XI, 351 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Problèmes inverses (équations différentielle) ram Traitement d'images - Mathématiques ram déconvolution inriac problème inverse inriac problème mal posé inriac restauration image inriac traitement image inriac équation différentielle inriac Mathematik Image processing Mathematics Inverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Inverse Methode (DE-588)4162226-1 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 s Inverse Methode (DE-588)4162226-1 s DE-604 Inverses Problem (DE-588)4125161-1 s Boccacci, Patrizia Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008277630&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertero, Mario Boccacci, Patrizia Introduction to inverse problems in imaging Problèmes inverses (équations différentielle) ram Traitement d'images - Mathématiques ram déconvolution inriac problème inverse inriac problème mal posé inriac restauration image inriac traitement image inriac équation différentielle inriac Mathematik Image processing Mathematics Inverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd Bildverarbeitung (DE-588)4006684-8 gnd Inverse Methode (DE-588)4162226-1 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4006684-8 (DE-588)4162226-1 |
| title | Introduction to inverse problems in imaging |
| title_auth | Introduction to inverse problems in imaging |
| title_exact_search | Introduction to inverse problems in imaging |
| title_full | Introduction to inverse problems in imaging Mario Bertero ; Patricia Boccacci |
| title_fullStr | Introduction to inverse problems in imaging Mario Bertero ; Patricia Boccacci |
| title_full_unstemmed | Introduction to inverse problems in imaging Mario Bertero ; Patricia Boccacci |
| title_short | Introduction to inverse problems in imaging |
| title_sort | introduction to inverse problems in imaging |
| topic | Problèmes inverses (équations différentielle) ram Traitement d'images - Mathématiques ram déconvolution inriac problème inverse inriac problème mal posé inriac restauration image inriac traitement image inriac équation différentielle inriac Mathematik Image processing Mathematics Inverse problems (Differential equations) Inverses Problem (DE-588)4125161-1 gnd Bildverarbeitung (DE-588)4006684-8 gnd Inverse Methode (DE-588)4162226-1 gnd |
| topic_facet | Problèmes inverses (équations différentielle) Traitement d'images - Mathématiques déconvolution problème inverse problème mal posé restauration image traitement image équation différentielle Mathematik Image processing Mathematics Inverse problems (Differential equations) Inverses Problem Bildverarbeitung Inverse Methode |
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