Astronomical Image and Data Analysis

292 Pages·2002·8.618 MB·English

by  Dr. Jean-Luc Starck, Professor Fionn Murtagh (auth.)

ASTRONOMY AND
~
ASTROPHYSICS LIBRARY
LIBRARY
Series Editors: I. Appenzeller, Heidelberg, Germany
G. Bomer, Garching, Germany
M. Harwit, Washington, DC, USA
R. Kippenhahn, Gottingen, Germany
J. Lequeux, Paris, France
V. Trimble, College Park, MD; and Irvine, CA, USA
Springer-Verlag
Berlin Heidelberg GmbH
ONLINE LIBRARY
Physics and Astronomy
http://www.springer.de/phys/
Jean-Luc Starck Fionn Murtagh
Astronomical Image
and Data Analysis
With 102 Figures, Including 27 Color Figures, and 10 Tables
i
Springer
Dr. Jean-Luc Starck
Centre d'Etudes de Saclay
Service d' Astrophysique
Orme des M6risiers
91191 Gif-sur- Yvette Cedex, France
Professor Fionn Murtagh
Queen's University Belfast
School of Computer Science
Belfast BT7 lNN, Northern Ireland, UK
Cover picture: Five-minute exposure (five 60-second dithered and stacked images), R filter, taken with CFH12K
wide-field camera (100 million pixels) at the primary focus ofthe CFHT in July 2000.
The image is from an extremely rich zone of our Galaxy, containing star formation regions, dark nebulae (molecular
c10uds and dust regions), emission nebulae (Ha regions), and evolved stars which are scattered throughout the field
in their two-dimensiona1 projection effect. This zone is in the constellation of Sagittarius. (©Canada-France-Hawaii
Telescope, J.-C. Cuillandre, 2000.)
Library of Congress Cataloging-in-PublicationData.
Starck, J.-L. (Jean-Luc), 1965-
Astronomical image and data ana1ysis / Jean-Luc Starck, Fionn Murtagh.
p. cm. - (Astronomy and astrophysics library, ISSN 0941-7834)
Inc1udes bibliographica1 references and index.
ISBN 978-3-662-04908-2 ISBN 978-3-662-04906-8 (eBook)
DOI 10.1007/978-3-662-04906-8
1. Imaging systems in astronomy-Data processing.
1. Murtagh, Fionn. II. Title. III. Series.
QB51.3145 S73 2002
522' .0285-dc21 2002074295
ISSN 0941-7834
ISBN 978-3-662-04908-2
This work is subject to copyright. All rights are reserved, whether the whole or par! of the material is concemed, spe
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© Springer-Verlag Berlin Heidelberg 2002
Originally published by Springer Berlin Heidelberg New York in 2002
Softcover reprint of the hardcover 1s t edition 2002
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Preface
When we consider the ever increasing amount of astronomical data available
to us, we can well say that the needs of modern astronomy are growing by
the day. Ever better observing facilities are in operation. The fusion of infor
mation leading to the coordination of observations is of central importance.
The methods described in this book can provide effective and efficient
ripostes to many of these issues. Much progress has been made in recent
years on the methodology front, in line with the rapid pace of evolution of
our technological infrastructures.
The central themes of this book are information and scale. The approach is
astronomy-driven, starting with real problems and issues to be addressed. We
then proceed to comprehensive theory, and implementations of demonstrated
efficacy.
The field is developing rapidly. There is little doubt that further important
papers, and books, will follow in the future.
Colleagues we would like to acknowledge include: Alexandre Aussem,
Albert Bijaoui, Franc;ois Bonnarel, Jonathan G. Campbell, Ghada Jammal,
Rene Gastaud, Pierre-Franc;ois Honore, Bruno Lopez, Mireille Louys, Clive
Page, Eric Pantin, Philippe Querre, Victor Racine, Jerome Rodriguez, and
Ivan Valtchanov.
The cover image is from Jean-Charles Cuillandre. It shows a 5-min ex
posure (5 60-s dithered and stacked images), R filter, taken with a CFH12K
wide-field camera (100 million pixels) at the primary focus of the CFHT in
July 2000. The image is from an extremely rich zone of our Galaxy, containing
star formation regions, dark nebulae (molecular clouds and dust regions),
emission nebulae (HaJ, and evolved stars which are scattered throughout the
field in their two-dimensional projection effect. This zone is in the constella
tion of Sagittarius.
Paris, Belfast J ean-Luc Starck,
June 2002 Fionn Murtagh
Contents
1. Introduction to Applications and Methods. . . . . . . . . . . . . . . . 1
1.1 Introduction........................................... 1
1.2 Transformation and Data Representation. . . . . . . . . . . . . . . . . . 3
1.2.1 Fourier Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Time-Frequency Representation. . . . . . . . . . . . . . . . . . . . 6
1.2.3 Time-Scale Representation: The Wavelet Transform .. 9
1.2.4 The Radon Transform ............................ 12
1.3 Mathematical Morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
1.4 Edge Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
1.4.1 First Order Derivative Edge Detection. . . . . . . . . . . . .. 15
1.4.2 Second Order Derivative Edge Detection ............ 19
1.5 Segmentation.......................................... 20
1.6 Pattern Recognition .................................... 21
1. 7 Summary.............................................. 25
2. Filtering.................................................. 27
2.1 Introduction........................................... 27
2.2 Multiscale Transforms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
a
2.2.1 The Trous Isotropic Wavelet Transform. . . . . . . . . . .. 29
2.2.2 Multiscale Transforms
Compared to Other Data Transforms ..... . . . . . . . . .. 30
2.2.3 Choice of Multiscale Transform .................... 32
2.2.4 The Multiresolution Support. . . . . . . . . . . . . . . . . . . . . .. 34
2.3 Significant Wavelet Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . .. 35
2.3.1 Definition....................................... 35
2.3.2 Noise Modeling .................................. 36
2.3.3 Automatic Estimation of Gaussian Noise. . . . . . . . . . .. 37
2.4 Filtering and Wavelet Coefficient Thresholding. . . . . . . . . . . .. 45
2.4.1 Thresholding.................................... 45
2.4.2 Iterative Filtering ................................ 46
2.4.3 Experiments..................................... 47
2.4.4 Iterative Filtering with a Smoothness Constraint ..... 49
2.5 Haar Wavelet Transform and Poisson Noise. . . . . . . . . . . . . . .. 51
2.5.1 Haar Wavelet Transform .......................... 52
VIII Contents
2.5.2 Poisson Noise and Haar Wavelet Coefficients. . . . . . . .. 52
2.5.3 Experiments..................................... 55
2.6 Summary.............................................. 58
3. Deconvolution............................................ 59
3.1 Introduction........................................... 59
3.2 The Deconvolution Problem ............................. 60
3.3 Linear Regularized Methods .... . . . . . . . . . . . . . . . . . . . . . . . .. 63
3.3.1 Least Squares Solution. . . . . . . . . . . . . . . . . . . . . . . . . . .. 63
3.3.2 Tikhonov Regularization. . . . . . . . . . . . . . . . . . . . . . . . .. 63
3.3.3 Generalization................................... 64
3.4 CLEAN............................................... 65
3.5 Bayesian Methodology ............................ . . . . .. 66
3.5.1 Definition....................................... 66
3.5.2 Maximum Likelihood with Gaussian Noise. . . . . . . . . .. 66
3.5.3 Gaussian Bayes Model. . . . . . . . . . . . . . . . . . . . . . . . . . .. 67
3.5.4 Maximum Likelihood with Poisson Noise. . . . . . . . . . .. 67
3.5.5 Poisson Bayes Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68
3.5.6 Maximum Entropy Method. . .. . . . . .. . . . . . . . . .. . . .. 68
3.5.7 Other Regularization Models. . . . . . . . . . . . . . . . . . . . . .. 69
3.6 Iterative Regularized Methods ........................... 70
3.6.1 Constraints...................................... 70
3.6.2 Jansson-Van Cittert Method. . . . . . . . . . . . . . . . . . . . . .. 71
3.6.3 Other Iterative Methods .......................... 71
3.7 Wavelet-Based Deconvolution. . . . . . . . .. . . . . . . . . .. . . . . .. .. 72
3.7.1 Introduction..................................... 72
3.7.2 Wavelet-Vaguelette Decomposition. . . . . .. . . . . . . . . .. 73
3.7.3 Regularization from the Multiresolution Support. . . .. 75
3.7.4 Wavelet CLEAN. . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . .. 79
3.7.5 Multiscale Entropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
3.8 Deconvolution and Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . .. 86
3.9 Super-Resolution....................................... 87
3.9.1 Definition....................................... 87
3.9.2 Gerchberg-Saxon-Papoulis Method. . . . . . . . . . . . . . . .. 87
3.9.3 Deconvolution with Interpolation. . . . . . . . . . . . . . . . . .. 88
3.9.4 Undersampled Point Spread Function. . . . . . . . . . . . . .. 89
3.9.5 Multiscale Support Constraint ..................... 90
3.10 Conclusions and Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 90
4. Detection................................................. 93
4.1 Introduction........................................... 93
4.2 From Images to Catalogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94
4.3 Multiscale Vision Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
4.3.1 Introduction..................................... 98
4.3.2 Multiscale Vision Model Definition ................. 99
Contents IX
4.3.3 From Wavelet Coefficients to Object Identification. . .. 99
4.3.4 Partial Reconstruction ............................ 102
4.3.5 Examples ....................................... 104
4.3.6 Application to ISOCAM Data Calibration ........... 106
4.4 Detection and Deconvolution ............................. 110
4.5 Conclusion ............................................ 112
4.6 Summary .............................................. 113
5. Image Compression ....................................... 115
5.1 Introduction ........................................... 115
5.2 Lossy Image Compression Methods ....................... 117
5.2.1 The Principle .................................... 117
5.2.2 Compression with Pyramidal Median Transform ..... 118
5.2.3 PMT and Image Compression ...................... 120
5.2.4 Compression Packages ............................ 123
5.2.5 Remarks on These Methods ....................... 124
5.3 Comparison ............................................ 126
5.3.1 Quality Assessment ............................... 126
5.3.2 Visual Quality ................................... 127
5.3.3 First Aladin Project Study ........................ 128
5.3.4 Second Aladin Project Study ...................... 131
5.3.5 Computation Time ............................... 136
5.3.6 Conclusion ...................................... 136
5.4 Lossless Image Compression ............................. 138
5.4.1 Introduction ..................................... 138
5.4.2 The Lifting Scheme ............................... 139
5.4.3 Comparison ..................................... 143
5.5 Large Images: Compression and Visualization .............. 144
5.5.1 Large Image Visualization Environment: LIVE ....... 144
5.5.2 Decompression by Scale and by Region .............. 146
5.5.3 The SAO-DS9 LIVE Implementation ............... 146
5.6 Summary .............................................. 149
6. Multichannel Data ........................................ 151
6.1 Introduction ........................................... 151
6.2 The Wavelet-Karhunen-Loeve Transform .................. 151
6.2.1 Definition ....................................... 151
6.2.2 Correlation Matrix and Noise Modeling ............. 152
6.2.3 Scale and Karhunen-Loeve Transform ............... 153
6.2.4 The WT-KLT Transform .......................... 154
6.2.5 The WT-KLT Reconstruction Algorithm ............ 155
6.3 Noise Modeling in the WT-KLT Space .................... 155
6.4 Multichannel Data Filtering ............................. 156
6.4.1 Introduction ..................................... 156
6.4.2 Reconstruction from a Subset of Eigenvectors ........ 156
X Contents
6.4.3 WT-KLT Coefficient Thresholding .................. 157
6.4.4 Example: Astronomical Source Detection ............ 158
6.5 The Haar-Multichannel Transform ........................ 158
6.6 Independent Component Analysis ........................ 159
6.7 Summary .............................................. 160
7. An Entropic Tour of Astronomical Data Analysis ......... 163
7.1 Introduction ........................................... 163
7.2 The Concept of Entropy ................................. 166
7.3 Multiscale Entropy ..................................... 172
7.3.1 Definition ....................................... 172
7.3.2 Signal and Noise Information ...................... 174
7.4 Multiscale Entropy Filtering ............................. 176
7.4.1 Filtering ........................................ 176
7.4.2 The Regularization Parameter ..................... 177
7.4.3 Use of a Model ................................... 179
7.4.4 The Multiscale Entropy Filtering Algorithm ......... 180
7.4.5 Optimization .................................... 181
7.4.6 Examples ....................................... 181
7.5 Deconvolution .......................................... 185
7.5.1 The Principle .................................... 185
7.5.2 The Parameters .................................. 186
7.5.3 Examples ....................................... 187
7.6 Multichannel Data Filtering ............................. 187
7.7 Background Fluctuation Analysis ......................... 190
7.8 Relevant Information in an Image ........................ 191
7.9 Multiscale Entropy and Optimal Compressibility ........... 192
7.10 Conclusions and Summary ............................... 194
8. Astronomical Catalog Analysis ........................... 197
8.1 Introduction ........................................... 197
8.2 Two-Point Correlation Function .......................... 198
8.2.1 Introduction ..................................... 198
8.2.2 Determining the 2-Point Correlation Function ........ 199
8.2.3 Error Analysis ................................... 200
8.2.4 Correlation Length Determination .................. 201
8.2.5 Creation of Random Catalogs ...................... 201
8.2.6 Examples ....................................... 202
8.3 Fractal Analysis ........................................ 206
8.3.1 Introduction ..................................... 206
8.3.2 The Hausdorff and Minkowski Measures ............. 207
8.3.3 The Hausdorff and Minkowski Dimensions ........... 208
8.3.4 Multifractality ................................... 209
8.3.5 Generalized Fractal Dimension ..................... 210
8.3.6 Wavelet and Multifractality ........................ 210