Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing

Content: 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    1.3. Method 7    1.4. Results 15    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, Gregory FRANCIUS, Jerome IDIER    2.1. Introduction 31    2.2. Atomic force microscopy 32    2.3. Data processing in AFM spectroscopy 40    2.4. Sparse approximation algorithms 43    2.5. Real data processing 49    2.6. Conclusion 52    2.7. Bibliography 53    CHAPTER 3. POLARIMETRIC IMAGE RESTORATION BY NON-LOCAL MEANS 57 Sylvain FAISAN, Francois 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    3.4. Results 72    3.5. Conclusion 77    3.6. Bibliography 78    CHAPTER 4. VIDEO PROCESSING AND REGULARIZED INVERSION METHODS 81 Guy LE BESNERAIS, Frederic CHAMPAGNAT    4.1. Introduction 81    4.2. Three applications 82    4.3. Dense image registration 88    4.4. A few achievements based on direct formulation 92    4.5. Conclusion 104    4.6. Bibliography 106    CHAPTER 5. BAYESIAN APPROACH IN PERFORMANCE MODELING: APPLICATION TO SUPERRESOLUTION 109 Frederic CHAMPAGNAT, Guy LE BESNERAIS, Caroline KULCSAR    5.1. Introduction 109    5.2. Performance modeling and Bayesian paradigm 111    5.3. Superresolution techniques behavior 113    5.4. Application examples 126    5.5. Real data processing 130    5.6. Conclusion 136    5.7. Bibliography 137    CHAPTER 6. LINE SPECTRA ESTIMATION FOR IRREGULARLY SAMPLED SIGNALS IN ASTROPHYSICS 141 Sebastien BOURGUIGNON, Herve CARFANTAN    6.1. Introduction 141    6.2. Periodogram, irregular sampling, maximum likelihood 144    6.3. Line spectra models: spectral sparsity 146    6.4. Prewhitening, CLEAN and greedy approaches 151    6.5. Global approach and convex penalization 155    6.6. Probabilistic approach for sparsity 159    6.7. Conclusion 164    6.8. Bibliography 165    CHAPTER 7. JOINT DETECTION-ESTIMATION IN FUNCTIONAL MRI 169 Philippe CIUCIU, Florence FORBES, Thomas VINCENT, Lotfi CHAARI    7.1. Introduction to functional neuroimaging 169    7.2. Joint detection-estimation of brain activity 171    7.3. Bayesian approach 178    7.4. Scheme for stochastic MCMC inference 183    7.5. Alternative variational inference scheme 184    7.6. Comparison of both types of solutions 190    7.7. Conclusion 194    7.8. Bibliography 195    CHAPTER 8. MCMC AND VARIATIONAL APPROACHES FOR BAYESIAN INVERSION IN DIFFRACTION IMAGING 201 Hacheme AYASSO, Bernard DUCHENE, Ali MOHAMMAD-DJAFARI    8.1. Introduction 201    8.2. Measurement configuration 204    8.3. The forward model 206    8.4. Bayesian inversion approach 211    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, Aurelia 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    9.5. Implementation of the variational Bayesian approach 236    9.6. Results 240    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, Cedric RICHARD    10.1. Introduction 251    10.2. State of the art: limitations of existing methods 252    10.3. Model-less target tracking 254    10.4. Simulation results 261    10.5. Conclusion 264    10.6. Bibliography 264    CHAPTER 11. ENTROPIES AND ENTROPIC CRITERIA 267 Jean-Francois BERCHER    11.1. Introduction 267    11.2. Some entropies in information theory 268    11.3. Source coding with escort distributions and Renyi bounds 273    11.4. A simple transition model 277    11.5. Minimization of the Renyi divergence and associated entropies 281    11.6. Bibliography 289    LIST OF AUTHORS 293    INDEX 297