Astronomical Image and Data Analysis

By: J. -L Starck, F. Murtagh

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Hardcover | 9 August 2006 | Edition Number 2

At a Glance

Hardcover
356 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 15.88 x 1.91

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Thisbookpresentsmaterialwhichismorealgorithmicallyorientedthanmost alternatives.Italsodealswithtopicsthatareatorbeyondthestateoftheart. Examples include practical and applicable wavelet and other multiresolution transform analysis. New areas are broached like the ridgelet and curvelet transforms. The reader will ?nd in this book an engineering approach to the interpretation of scienti?c data. Compared to the 1st Edition, various additions have been made throu- out, and the topics covered have been updated. The background or en- ronment of this book's topics include continuing interest in e-science and the virtual observatory, which are based on web based and increasingly web service based science and engineering. Additional colleagues whom we would like to acknowledge in this 2nd edition include: Bedros Afeyan, Nabila Aghanim, Emmanuel Cand` es, David Donoho, Jalal Fadili, and Sandrine Pires, We would like to particularly - knowledge Olivier Forni who contributed to the discussion on compression of hyperspectral data, Yassir Moudden on multiwavelength data analysis and Vicent Mart´ ?nez on the genus function. The cover image to this 2nd edition is from the Deep Impact project. It was taken approximately 8 minutes after impact on 4 July 2005 with the CLEAR6 ?lter and deconvolved using the Richardson-Lucy method. We thank Don Lindler, Ivo Busko, Mike A'Hearn and the Deep Impact team for the processing of this image and for providing it to us.

Industry Reviews

"This book is an authoritative and thorough account of numerous mathematical techniques used by research astronomers and I can strongly recommend it for those purposes." (C.R. Kitchin, Astronomy Now, Oct. 2003)

"The book addresses not only students and professional astronomers and astrophysicists, but also serious amateur astronomers and specialists in earth observation, medical imaging, and data mining." (Europe & Astronomy, 905, 2003)

"The phenomenal amounts of data produced by modern telescopes require powerful tools to extract whatever valuable nuggets of information they contain from the dross of unwanted signal and noise. Computer power available to reduce the data is barely sufficient to keep pace. This monograph is aimed at solving these problems by a variety of different methods. [...] The book includes a number of well-chosen illustrative examples, some based on real, and others on artificial data. It also has a substantial bibliography. However it is not a guide to the several excellent reduction packages currently available. Rather it is a thorough investigation of how astronomical images can be modelled and how the maximum information can be extracted from the noise, and for this it can be recommended." (The Observatory, 123/1174, 2003)

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You Can Find This Book In

Non-Fiction Engineering & Technology Other Technologies & Applied Sciences Applied Optics Imaging Systems & Technology Science Astronomy, Space & Time Astronomical Observation & Observatories Computing & I.T.Databases Data Capture & Analysis Computer Science

Image Processing Digital Signal Processing (DSP)Physics Applied Physics Astrophysics

Introduction to Applications and Methods	p. 1
Introduction	p. 1
Transformation and Data Representation	p. 3
Fourier Analysis	p. 5
Time-Frequency Representation	p. 6
Time-Scale Representation: The Wavelet Transform	p. 9
The Radon Transform	p. 12
Mathematical Morphology	p. 12
Edge Detection	p. 15
First Order Derivative Edge Detection	p. 15
Second Order Derivative Edge Detection	p. 19
Segmentation	p. 20
Pattern Recognition	p. 21
Summary	p. 25
Filtering	p. 27
Introduction	p. 27
Multiscale Transforms	p. 29
The à Trous Isotropic Wavelet Transform	p. 29
Multiscale Transforms Compared to Other Data Transforms	p. 30
Choice of Multiscale Transform	p. 32
The Multiresolution Support	p. 34
Significant Wavelet Coefficients	p. 35
Definition	p. 35
Noise Modeling	p. 36
Automatic Estimation of Gaussian Noise	p. 37
Filtering and Wavelet Coefficient Thresholding	p. 45
Thresholding	p. 45
Iterative Filtering	p. 46
Experiments	p. 47
Iterative Filtering with a Smoothness Constraint	p. 49
Haar Wavelet Transform and Poisson Noise	p. 51
Haar Wavelet Transform	p. 52
Poisson Noise and Haar Wavelet Coefficients	p. 52
Experiments	p. 55
Summary	p. 58
Deconvolution	p. 59
Introduction	p. 59
The Deconvolution Problem	p. 60
Linear Regularized Methods	p. 63
Least Squares Solution	p. 63
Tikhonov Regularization	p. 63
Generalization	p. 64
CLEAN	p. 65
Bayesian Methodology	p. 66
Definition	p. 66
Maximum Likelihood with GaussianNoise	p. 66
Gaussian Bayes Model	p. 67
Maximum Likelihood with Poisson Noise	p. 67
Poisson Bayes Model	p. 68
Maximum Entropy Method	p. 68
Other Regularization Models	p. 69
Iterative Regularized Methods	p. 70
Constraints	p. 70
Jansson-Van Cittert Method	p. 71
Other Iterative Methods	p. 71
Wavelet-Based Deconvolution	p. 72
Introduction	p. 72
Wavelet-Vaguelette Decomposition	p. 73
Regularization from the Multiresolution Support	p. 75
Wavelet CLEAN	p. 79
Multiscale Entropy	p. 84
Deconvolution and Resolution	p. 86
Super-Resolution	p. 87
Definition	p. 87
Gerchberg-Saxon-Papoulis Method	p. 87
Deconvolution with Interpolation	p. 88
Undersampled Point Spread Function	p. 89
Multiscale Support Constraint	p. 90
Conclusions and Summary	p. 90
Detection	p. 93
Introduction	p. 93
From Images to Catalogs	p. 94
Multiscale Vision Model	p. 98
Introduction	p. 98
Multiscale Vision Model Definition	p. 99
From Wavelet Coefficients to Object Identification	p. 99
Partial Reconstruction	p. 102
Examples	p. 104
Application to ISOCAM Data Calibration	p. 106
Detection and Deconvolution	p. 110
Conclusion	p. 112
Summary	p. 113
Image Compression	p. 115
Introduction	p. 115
Lossy Image Compression Methods	p. 117
The Principle	p. 117
Compression with Pyramidal Median Transform	p. 118
PMT and Image Compression	p. 120
Compression Packages	p. 123
Remarks on These Methods	p. 124
Comparison	p. 126
Quality Assessment	p. 126
Visual Quality	p. 127
First Aladin Project Study	p. 128
Second Aladin Project Study	p. 131
Computation Time	p. 136
Conclusion	p. 136
Loss less Image Compression	p. 138
Introduction	p. 138
The Lifting Scheme	p. 139
Comparison	p. 143
Large Images: Compression and Visualization	p. 144
Large Image Visualization Environment: LIVE	p. 144
Decompression by Scale and by Region	p. 146
TheSAO-DS9 LIVE Implementation	p. 146
Summary	p. 149
Multichannel Data	p. 151
Introduction	p. 151
The Wavelet-Karhunen-Loeve Transform	p. 151
Definition	p. 151
Correlation Matrix and Noise Modeling	p. 152
Scale and Karhunen-Loaeve Transform	p. 153
The WT-KLT Transform	p. 154
TheWT-KLT Reconstruction Algorithm	p. 155
Noise Modeling in the WT-KLT Space	p. 155
Multichannel Data Filtering	p. 156
Introduction	p. 156
Reconstruction from a Subset of Eigenvectors	p. 156
WT-KLT Coefficient Thresholding	p. 157
Example: Astronomical Source Detection	p. 158
The Haar-Multichannel Transform	p. 158
Independent Component Analysis	p. 159
Summary	p. 160
An Entropic Tour of Astronomical Data Analysis	p. 163
Introduction	p. 163
The Concept of Entropy	p. 166
Multiscale Entropy	p. 172
Definition	p. 172
Signal and Noise Information	p. 174
Multiscale Entropy Filtering	p. 176
Filtering	p. 176
The Regularization Parameter	p. 177
Use of a Model	p. 179
The Multiscale Entropy Filtering Algorithm	p. 180
Optimization	p. 181
Examples	p. 181
Deconvolution	p. 185
The Principle	p. 185
The Parameters	p. 186
Examples	p. 187
Multichannel Data Filtering	p. 187
Background Fluctuation Analysis	p. 190
Relevant Information in an Image	p. 191
Multiscale Entropy and Optimal Compressibility	p. 192
Conclusions and Summary	p. 194
Astronomical Catalog Analysis	p. 197
Introduction	p. 197
Two-Point Correlation Function	p. 198
Introduction	p. 198
Determiningthe2-PointCorrelationFunction	p. 199
Error Analysis	p. 200
Correlation Length Determination	p. 201
Creation of Random Catalogs	p. 201
Examples	p. 202
Fractal Analysis	p. 206
Introduction	p. 206
The Hausdorff and Minkowski Measures	p. 207
The Hausdorff and Minkowski Dimensions	p. 208
Multifractality	p. 209
Generalized Fractal Dimension	p. 210
Wavelet and Multifractality	p. 210
Spanning Trees and Graph Clustering	p. 214
Voronoi Tessellation and Percolation	p. 216
Model-Based Clustering	p. 216
Modeling of Signal and Noise	p. 217
Application to Thresholding	p. 218
Wavelet Analysis	p. 219
Nearest Neighbor Clutter Removal	p. 221
Summary	p. 222
Multiple Resolution in Data Storage and Retrieval	p. 223
Introduction	p. 223
Wavelets in Database Management	p. 223
Fast Cluster Analysis	p. 225
Nearest Neighbor Finding on Graphs	p. 227
Cluster-Based User Interfaces	p. 228
Images from Data	p. 230
Matrix Sequencing	p. 230
Filtering Hypertext	p. 233
Clustering Document-TermData	p. 235
Summary	p. 239
Towards the Virtual Observatory	p. 241
Data and Information	p. 241
The Information Handling Challenges Facing Us	p. 243
à Trous Wavelet Transform	p. 245
Picard Iteration	p. 251
Wavelet Transform Using the Fourier Transform	p. 253
Derivative Needed for the Minimization	p. 257
Generalization of the Derivative Needed for the Minimization	p. 261
Software and Related Developments	p. 263
Bibliography	p. 265
Index	p. 284
Table of Contents provided by Publisher. All Rights Reserved.

Astronomical Image and Data Analysis

At a Glance

Hardcover

Industry Reviews

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