Cover -- Title Page -- Copyright -- Contents -- Introduction -- I.1. Bibliography -- 1: 3D Reconstruction in X-ray Tomography: Approach Example for Clinical Data Processing -- 1.1. Introduction -- 1.2. Problem statement -- 1.2.1. Data formation models -- 1.2.2. Estimators -- 1.2.3. Algorithms -- 1.3. Method -- 1.3.1. Data formation models -- 1.3.2. Estimator -- 1.3.3. Minimization method -- 1.3.3.1. Algorithm selection -- 1.3.3.2. Minimization procedure -- 1.3.4. Implementation of the reconstruction procedure -- 1.4. Results -- 1.4.1. Comparison of minimization algorithms -- 1.4.2. Using a region of interest in reconstruction -- 1.4.3. Consideration of the polyenergetic character of the X-ray source -- 1.4.3.1. Simulated data in 2D -- 1.4.3.2. Real data in 3D -- 1.5. Conclusion -- 1.6. Acknowledgments -- 1.7. Bibliography -- 2: Analysis of Force-Volume Images in Atomic Force Microscopy Using Sparse Approximation -- 2.1. Introduction -- 2.2. Atomic force microscopy -- 2.2.1. Biological cell characterization -- 2.2.2. AFM modalities -- 2.2.2.1. Isoforce and isodistance images -- 2.2.2.2. Force spectroscopy -- 2.2.2.3. Force-volume imaging -- 2.2.3. Physical piecewise models -- 2.2.3.1. Approach phase models -- 2.2.3.2. Retraction phase models -- 2.3. Data processing in AFM spectroscopy -- 2.3.1. Objectives and methodology in signal processing -- 2.3.1.1. Detection of the regions of interest -- 2.3.1.2. Parametric model fitting -- 2.3.2. Segmentation of a force curve by sparse approximation -- 2.3.2.1. Detecting jumps in a signal -- 2.3.2.2. Joint detection of discontinuities at different orders -- 2.3.2.3. Scalar and vector variable selection -- 2.4. Sparse approximation algorithms -- 2.4.1. Minimization of a mixed l2-l0 criterion -- 2.4.2. Dedicated algorithms -- 2.4.3. Joint detection of discontinuities -- 2.4.3.1. Construction of the dictionary.

2.4.3.2. Selection of scalar variables -- 2.4.3.3. Selection of vector variables -- 2.5. Real data processing -- 2.5.1. Segmentation of a retraction curve: comparison of strategies -- 2.5.2. Retraction curve processing -- 2.5.3. Force-volume image processing in the approach phase -- 2.6. Conclusion -- 2.7. Bibliography -- 3: Polarimetric Image Restoration by Non-local Means -- 3.1. Introduction -- 3.2. Light polarization and the Stokes-Mueller formalism -- 3.3. Estimation of the Stokes vectors -- 3.3.1. Estimation of the Stokes vector in a pixel -- 3.3.1.1. Problem formulation -- 3.3.1.2. Properties of the constrained optimization problem -- 3.3.1.3. Optimization algorithm -- 3.3.2. Non-local means filtering -- 3.3.3. Adaptive non-local means filtering -- 3.3.3.1. The function φ -- 3.3.3.2. Patches size and shape -- 3.3.4. Application to the estimation of Stokes vectors -- 3.4. Results -- 3.4.1. Results with synthetic data -- 3.4.1.1. Synthetic data and context evaluation presentation -- 3.4.1.2. Results -- 3.4.1.3. Significance of the proposed method for the estimation of the weights -- 3.4.2. Results with real data -- 3.5. Conclusion -- 3.6. Bibliography -- 4: Video Processing and Regularized Inversion Methods -- 4.1. Introduction -- 4.2. Three applications -- 4.2.1. PIV and estimation of optical flow -- 4.2.2. Multiview stereovision -- 4.2.3. Superresolution and non-translational motion -- 4.3. Dense image registration -- 4.3.1. Direct formulation -- 4.3.2. Variational formulation -- 4.3.3. Extension of direct formulation for multiview processing -- 4.4. A few achievements based on direct formulation -- 4.4.1. Dense optical flow by correlation of local window -- 4.4.1.1. Lucas-Kanade exact approach -- 4.4.1.2. IWS scheme -- 4.4.1.3. FOLKI algorithm -- 4.4.2. Occlusion management in multiview stereovision.

4.4.2.1. A regularized approach of the elevation estimation -- 4.4.2.2. Occlusion management by typical visibility -- 4.4.3. Direct models for SR -- 4.4.3.1. A calculation in object geometry -- 4.4.3.2. A calculation in sensor geometry -- 4.4.3.3. Shift-and-add model -- 4.5. Conclusion -- 4.6. Bibliography -- 5: Bayesian Approach in Performance Modeling: Application to Superresolution -- 5.1. Introduction -- 5.1.1. The hiatus between performance modeling and Bayesian inversion -- 5.1.2. Chapter organization -- 5.2. Performance modeling and Bayesian paradigm -- 5.2.1. An empirical performance evaluation tool -- 5.2.2. Usefulness and limits of a performance evaluation tool -- 5.2.3. Bayesian formalism -- 5.3. Superresolution techniques behavior -- 5.3.1. Superresolution -- 5.3.2. SR methods performance: known facts -- 5.3.2.1. Condition number of forward model and regularization -- 5.3.2.2. Influential parameters -- 5.3.2.3. Registration error -- 5.3.3. An SR experiment -- 5.3.4. Performance model and properties -- 5.3.4.1. Data and processing models -- 5.3.4.2. Input models -- 5.3.4.3. Performance measure -- 5.3.4.4. Discussion -- 5.4. Application examples -- 5.4.1. Behavior of the optimal filter with regard to the number of images -- 5.4.2. Characterization of an approximation: shifts rounding -- 5.5. Real data processing -- 5.5.1. A concrete measure to improve the resolution: the RER -- 5.5.2. Empirical validation and application field -- 5.6. Conclusion -- 5.7. Bibliography -- 6: Line Spectra Estimation for Irregularly Sampled Signals in Astrophysics -- 6.1. Introduction -- 6.2. Periodogram, irregular sampling and maximum likelihood -- 6.3. Line spectra models: spectral sparsity -- 6.3.1. An inverse problem with sparsity prior information -- 6.3.2. Difficulties in terms of sparse approximation -- 6.4. Prewhitening, CLEAN and greedy approaches.

6.4.1. Standard greedy algorithms -- 6.4.1.1. Matching pursuit -- 6.4.1.2. Orthogonal matching pursuit -- 6.4.1.3. Orthogonal least squares -- 6.4.2. A more complete iterative method: single best replacement -- 6.4.3. CLEAN-based methods -- 6.5. Global approach and convex penalization -- 6.5.1. Significance of l1 penalization in C -- 6.5.2. Existence and uniqueness -- 6.5.3. Minimizer and regularization parameter analytical characterization -- 6.5.4. Amplitude bias and a posteriori corrections -- 6.5.5. Hermitian symmetry and specificity of the zero frequency -- 6.5.6. Optimization algorithms -- 6.5.7. Results -- 6.6. Probabilistic approach for sparsity -- 6.6.1. Bernoulli-Gaussian model for spectral analysis -- 6.6.2. A structure adapted to the use of MCMC methods -- 6.6.3. An extended BG model for improved accuracy -- 6.6.4. Stochastic simulation and estimation -- 6.6.5. Results -- 6.7. Conclusion -- 6.8. Bibliography -- 7: Joint Detection-Estimation in Functional MRI -- 7.1. Introduction to functional neuroimaging -- 7.2. Joint detection-estimation of brain activity -- 7.2.1. Detection and estimation: two interdependent issues -- 7.2.2. Hemodynamics physiological hypotheses -- 7.2.3. Spatially variable convolutive model -- 7.2.4. Regional generative model -- 7.3. Bayesian approach -- 7.3.1. Likelihood -- 7.3.2. A priori distributions -- 7.3.2.1. Hemodynamic response function (HRF) -- 7.3.2.2. Neural response levels (NRL) -- 7.3.2.3. Mixture hyperparameters -- 7.3.2.4. Noise and derivatives -- 7.3.3. A posteriori distribution -- 7.4. Scheme for stochastic MCMC inference -- 7.4.1. HRF and NRLs simulation -- 7.4.2. Unsupervised spatial and spatially adaptive regularization -- 7.5. Alternative variational inference scheme -- 7.5.1. Motivations and foundations -- 7.5.2. Variational EM algorithm -- 7.6. Comparison of both types of solutions.

7.6.1. Experiments on simulated data -- 7.6.2. Experiments on real data -- 7.7. Conclusion -- 7.8. Bibliography -- 8: MCMC and Variational Approaches for Bayesian Inversion in Diffraction Imaging -- 8.1. Introduction -- 8.2. Measurement configuration -- 8.2.1. The microwave device -- 8.2.2. The optical device -- 8.3. The forward model -- 8.3.1. The microwave case -- 8.3.2. The optical case -- 8.3.3. The discrete model -- 8.3.3.1. The observation matrix -- 8.3.3.2. The coupling matrix -- 8.3.4. Validation of the forward model -- 8.4. Bayesian inversion approach -- 8.4.1. The MCMC sampling method -- 8.4.2. The VBA method -- 8.4.3. Initialization, progress and convergence of the algorithms -- 8.5. Results -- 8.6. Conclusions -- 8.7. Bibliography -- 9: Variational Bayesian Approach and Bi-Model for the Reconstruction-Separation of Astrophysics Components -- 9.1. Introduction -- 9.2. Variational Bayesian methodology -- 9.3. Exponentiated gradient for variational Bayesian -- 9.4. Application: reconstruction-separation of astrophysical components -- 9.4.1. Direct model -- 9.4.2. A Priori distributions -- 9.4.3. A posteriori distribution -- 9.5. Implementation of the variational Bayesian approach -- 9.5.1. Separability study -- 9.5.2. Update of the approximation distributions -- 9.5.2.1. Update of the a distribution -- 9.5.2.2. Update of the p distribution -- 9.5.2.3. Update of the s distribution -- 9.5.2.4. Update of the o distribution -- 9.6. Results -- 9.6.1. Simulated data -- 9.6.1.1. Realistic simulation -- 9.6.1.2. Study of the peaks reconstruction -- 9.6.2. Real data -- 9.7. Conclusion -- 9.8. Bibliography -- 10: Kernel Variational Approach for Target Tracking in a Wireless Sensor Network -- 10.1. Introduction -- 10.2. State of the art: limitations of existing methods -- 10.3. Model-less target tracking.

10.3.1. Construction of the likelihood by matrix regression.