Regularization and Bayesian methods for inverse problems in signal and image processing (London; Hoboken, 2015). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаRegularization and Bayesian methods for inverse problems in signal and image processing / ed. by J.-F.Giovannelli, J.Idier. - London: ISTE; Hoboken: Wiley, 2015. - xv, 299 p.: ill. - (Digital signal and image processing series). - ISBN 978-1-84821-637-2
 

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Оглавление / Contents
 
Introduction ................................................... xi
     Jean-Francois Giovannelli and Jerome Idier

Chapter 1. 3D Reconstruction in X-ray Tomography: Approach
Example for Clinical Data Processing ............................ 1
Yves Goussard
1.1  Introduction ............................................... 1
1.2  Problem statement .......................................... 2
     1.2.1  Data formation models ............................... 2
     1.2.2  Estimators .......................................... 5
     1.2.3  Algorithms .......................................... 5
1.3  Method ..................................................... 7
     1.3.1  Data formation models ............................... 7
     1.3.2  Estimator .......................................... 10
     1.3.3  Minimization method ................................ 11
     1.3.4  Implementation of the reconstruction procedure ..... 14
1.4  Results ................................................... 15
     1.4.1  Comparison of minimization algorithms .............. 15
     1.4.2  Using a region of interest in reconstruction ....... 18
     1.4.3  Consideration of the polyenergetic character of
            the source ......................................... 21
1.5  Conclusion ................................................ 26
1.6  Acknowledgments ........................................... 27
1.7  Bibliography .............................................. 28

Chapter 2. Analysis of Force-Volume Images in Atomic Force
Microscopy Using Sparse Approximation .......................... 31
Charles Soussen, David Brie, Grégory Francius, Jérôme Idier
2.2  Atomic force microscopy ................................... 32
     2.2.1  Biological cell characterization ................... 32
     2.2.2  AFM modalities ..................................... 33
     2.2.3  Physical piecewise models  ......................... 37
2.3  Data processing in AFM spectroscopy ....................... 40
     2.3.1  Objectives and methodology in signal processing  ... 40
     2.3.2  Segmentation of a force curve by sparse 
            approximation ...................................... 41
2.4  Sparse approximation algorithms ........................... 43
     2.4.1  Minimization of a mixed ℓ2-ℓ0 criterion ............ 44
     2.4.2  Dedicated algorithms ............................... 44
     2.4.3  Joint detection of discontinuities ................. 46
2.5  Real data processing ...................................... 49
     2.5.1  Segmentation of a retraction curve: comparison of
            strategies ......................................... 49
     2.5.2  Retraction curve processing ........................ 50
     2.5.3  Force-volume image processing in the approach
            phase .............................................. 52
2.6  Conclusion ................................................ 52
2.7  Bibliography .............................................. 53

Chapter 3. Polarimetric Image Restoration by Non-local
Means .......................................................... 57
Sylvain Faisan, François Rousseau, Christian Heinrich, Jihad
Zallat
3.1  Introduction .............................................. 57
3.2  Light polarization and the Stokes-Mueller formalism ....... 58
3.3  Estimation of the Stokes vectors .......................... 61
     3.3.1  Estimation of the Stokes vector in a pixel ......... 61
     3.3.2  Non-local means filtering .......................... 64
     3.3.3  Adaptive non-local means filtering ................. 66
     3.3.4  Application to the estimation of Stokes vectors .... 69
3.4  Results ................................................... 72
     3.4.1  Results with synthetic data ........................ 72
     3.4.2  Results with real data ............................. 75
3.5  Conclusion ................................................ 77
3.6  Bibliography .............................................. 78

Chapter 4. Video Processing and Regularized Inversion Methods .. 81
Guy Le Besnerais, Frédéric Champagnat
4.1  Introduction .............................................. 81
4.2  Three applications ........................................ 82
     4.2.1  PIV and estimation of optical flow ................. 82
     4.2.2  Multiview stereovision ............................. 84
     4.2.3  Superresolution and non-translational motion ....... 86
4.3  Dense image registration  ................................. 88
     4.3.1  Direct formulation ................................. 90
     4.3.2  Variational formulation ............................ 91
     4.3.3  Extension of direct formulation for multiview
            processing ......................................... 92
4.4  A few achievements based on direct formulation ............ 92
     4.4.1  Dense optical flow by correlation of local window .. 92
     4.4.2  Occlusion management in multiview stereovision ..... 97
     4.4.3  Direct models for SR ............................... 99
4.5  Conclusion ............................................... 104
4.6  Bibliography ............................................. 106

Chapter 5. Bayesian Approach in Performance Modeling:
Application to SuperResolution ................................ 109
Frédéric Champagnat, Guy Le Besnerais, Caroline Kulcsár
5.1  Introduction ............................................. 109
     5.1.1  The hiatus between performance modeling and 
            Bayesian inversion ................................ 109
     5.1.2  Chapter organization .............................. 110
5.2  Performance modeling and Bayesian paradigm ............... 111
     5.2.1  An empirical performance evaluation tool .......... 111
     5.2.2  Usefulness and limits of a performance 
            evaluation tool ................................... 111
     5.2.3  Bayesian formalism ................................ 113
5.3  Superresolution techniques behavior ...................... 113
     5.3.1  Superresolution ................................... 114
     5.3.2  SR methods performance: known facts ............... 115
     5.3.3  An SR experiment .................................. 117
     5.3.4  Performance model and properties .................. 122
5.4  Application examples ..................................... 126
     5.4.1  Behavior of the optimal filter with regard to the
            number of images .................................. 127
     5.4.2  Characterization of an approximation: shifts
            rounding .......................................... 129
5.5  Real data processing ..................................... 130
     5.5.1  A concrete measure to improve the resolution: the
            RER ............................................... 132
     5.5.2  Empirical validation and application field ........ 134
5.6  Conclusion ............................................... 136
5.7  Bibliography ............................................. 137

Chapter 6. Line Spectra Estimation for Irregularly Sampled
Signals in Astrophysics ....................................... 141
Sébastien Bourguignon, Hervé Carfantan
6.1  Introduction ............................................. 141
6.2  Periodogram, irregular sampling, maximum likelihood ...... 144
6.3  Line spectra models: spectral sparsity ................... 146
     6.3.1  An inverse problem with sparsity prior 
            information ....................................... 147
     6.3.2  Difficulties in terms of sparse approximation ..... 149
6.4  Prewhitening, CLEAN and greedy approaches ................ 151
     6.4.1  Standard greedy algorithms ........................ 151
     6.4.2  A more complete iterative method: single best
            replacement ....................................... 153
     6.4.3  CLEAN-based methods ............................... 154
6.5  Global approach and convex penalization .................. 155
     6.5.1  Significance of ℓ1 penalization in fig.1 .............. 156
     6.5.2  Existence and uniqueness .......................... 156
     6.5.3  Minimizer and regularization parameter
            characterization .................................. 157
     6.5.4  Amplitude bias and a posteriori corrections ....... 157
     6.5.5  Hermitian symmetry and specificity of the zero
            frequency ......................................... 158
     6.5.6  Optimization algorithms ........................... 158
     6.5.7  Results ........................................... 159
6.6  Probabilistic approach for sparsity ...................... 159
     6.6.1  Bernoulli-Gaussian model for spectral analysis .... 160
     6.6.2  A structure adapted to the use of MCMC methods .... 161
     6.6.3  An extended BG model for improved accuracy ........ 162
     6.6.4  Stochastic simulation and estimation .............. 162
     6.6.5  Results  .......................................... 163
6.7  Conclusion ............................................... 164
6.8  Bibliography ............................................. 165

Chapter 7. Joint Detection-Estimation in Functional MRI ....... 169
Philippe Сiuсiu, Florence Forbes, Thomas Vincent, Lotfi Chaari
7.1  Introduction to functional neuroimaging .................. 169
7.2  Joint detection-estimation of brain activity  ............ 171
     7.2.1  Detection and estimation: two interdependent 
            issues ............................................ 171
     7.2.2  Hemodynamics physiological hypotheses ............. 173
     7.2.3  Spatially variable convolutive model .............. 175
     7.2.4  Regional generative model ......................... 176
7.3  Bayesian approach ........................................ 178
     7.3.1  Likelihood  ....................................... 178
     7.3.2  A priori distributions ............................ 178
     7.3.3  A posteriori distribution ......................... 182
7.4  Scheme for stochastic MCMC inference ..................... 183
     7.4.1  HRF and NRLs simulation ........................... 183
     7.4.2  Unsupervised spatial and spatially adaptive
            regularization .................................... 184
7.5  Alternative variational inference scheme ................. 184
     7.5.1  Motivations and foundations ....................... 184
     7.5.2  Variational EM algorithm .......................... 186
7.6  Comparison of both types of solutions .................... 190
     7.6.1  Experiments on simulated data ..................... 190
     7.6.2  Experiments on real data  ......................... 193
7.7  Conclusion ............................................... 194
7.8  Bibliography ............................................. 195

Chapter 8. MCMC and Variational Approaches for Bayesian
Inversion in Diffraction Imaging .............................. 201
Hacheme Ayasso, Bernard Duchène, Ali Mohammad-Djafari
8.1  Introduction ............................................. 201
8.2  Measurement configuration ................................ 204
     8.2.1  The microwave device .............................. 204
     8.2.2  The optical device ................................ 205
8.3  The forward model ........................................ 206
     8.3.1  The microwave case ................................ 207
     8.3.2  The optical case .................................. 207
     8.3.3  The discrete model ................................ 208
     8.3.4  Validation of the forward model ................... 210
8.4  Bayesian inversion approach .............................. 211
     8.4.1  The MCMC sampling method .......................... 213
     8.4.2  The VBA method .................................... 214
     8.4.3  Initialization, progress and convergence of the
            algorithms ........................................ 217
8.5  Results .................................................. 220
8.6  Conclusions .............................................. 220
8.7  Bibliography ............................................. 222

Chapter 9. Variational Bayesian Approach and Bi-Model for the
Reconstruction-Separation of Astrophysics Components .......... 225
Thomas Rodet, Aurélia Fraysse, Hacheme Ayasso
9.1  Introduction ............................................. 225
9.2  Variational Bayesian methodology ......................... 228
9.3  Exponentiated gradient for variational Bayesian .......... 229
9.4  Application: reconstruction-separation of astrophysical
     components ............................................... 232
     9.4.1  Direct model ...................................... 232
     9.4.2  A priori distributions ............................ 234
     9.4.3  A posteriori distribution ......................... 235
9.5  Implementation of the variational Bayesian approach ...... 236
     9.5.1  Separability study ................................ 236
     9.5.2  Update of the approximation distributions ......... 236
9.6  Results .................................................. 240
     9.6.1  Simulated data .................................... 241
     9.6.2  Real data ......................................... 244
9.7  Conclusion ............................................... 246
9.8  Bibliography ............................................. 246

Chapter 10. Kernel Variational Approach for Target Tracking in
a Wireless Sensor Network ..................................... 251
Hichem Snoussi, Paul Honeine, Cédric Richard
10.1 Introduction ............................................. 251
10.2 State of the art: limitations of existing methods ........ 252
10.3 Model-less target tracking ............................... 254
     10.3.1 Construction of the likelihood by matrix 
            regression ........................................ 255
     10.3.2 Variational filtering for the tracking of mobile
            objects ........................................... 258
10.4 Simulation results ....................................... 261
10.5 Conclusion ............................................... 264
10.6 Bibliography ............................................. 264

Chapter 11. Entropies and Entropic Criteria ................... 267
Jean-François Bercher
11.1 Introduction ............................................. 267
11.2 Some entropies in information theory ..................... 268
     11.2.1 Main properties and definitions ................... 268
     11.2.2 Entropies and divergences in the continuous case .. 270
     11.2.3 Maximum entropy ................................... 272
     11.2.4 Escort distributions .............................. 272
11.3 Source coding with escort distributions and Renyi bounds . 273
     11.3.1 Source coding ..................................... 274
     11.3.2 Source coding with Campbell measure ............... 274
     11.3.3 Source coding with escort mean  ................... 275
11.4 A simple transition model ................................ 277
     11.4.1 The model ......................................... 277
     11.4.2 The Renyi divergence as a consequence ............. 279
     11.4.3 Fisher information for the parameter q ............ 279
     11.4.4 Distribution inference with generalized moment
            constraint ........................................ 281
11.5 Minimization of the Renyi divergence and associated
     entropies ................................................ 281
     11.5.1 Minimization under generalized moment constraint .. 282
     11.5.2 A few properties of the partition functions ....... 283
     11.5.3 Entropic functionals derived from the Renyi
            divergence ........................................ 285
     11.5.4 Entropic criteria ................................. 287
11.6 Bibliography ............................................. 289
     List of Authors .......................................... 293

Index ......................................................... 297


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