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Banach, Fréchet, Hilbert and Neumann Spaces

Analysis for PDEs Set Volume 1

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Data Treatment in Environmental Sciences

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

Edited by Jean-François Giovannelli, University of Bordeaux, France Jérôme Idier, IRCCyN, Nantes, France

ISBN: 9781848216372

Publication Date: February 2015   Hardback   322 pp.

145.00 USD

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The solution of inverse problems is an unavoidable step in the signal and image processing chain, situated between data acquisition and decision making. Various inversion problems are presented by the authors of this book, such as tomography, detection-estimation, multi-resolution analysis, moving object tracking, and sparse approximations.
Recent mathematical concepts and tools in information theory, optimization, Bayesian inference and statistical modeling are put into practice in these different contexts. Each chapter is devoted to a widely developed and documented application.
Through various perspectives, a vast number of fields is covered: medical and biological imaging, astronomy, non-destructive evaluation, video processing, digital communications, sensor networks, etc.


1. 3D Reconstruction in X-ray Tomography: Approach Example for Clinical Data Processing, Yves Goussard.
2. Analysis of Force-Volume Images in Atomic Force Microscopy Using Sparse Approximation, Charles Soussen, David Brie, Grégory Francius, Jérôme Idier.
3. Polarimetric Image Restoration by Non-local Means, Sylvain Faisan, François Rousseau, Christian Heinrich, Jihad Zallat.
4. Video Processing and Regularized Inversion Methods, Guy Le Besnerais, Frédéric Champagnat.
5. Bayesian Approach in Performance Modeling: Application to Superresolution, Frédéric Champagnat, Guy Le Besnerais, Caroline Kulcsár.
6. Line Spectra Estimation for Irregularly Sampled Signals in Astrophysics, Sébastien Bourguignon, Hervé Carfantan.
7. Joint Detection-Estimation in Functional MRI, Philippe Ciuciu, Florence Forbes, Thomas Vincent, Lotfi Chaari.
8. MCMC and Variational Approaches for Bayesian Inversion in Diffraction Imaging, Hacheme Ayasso, Bernard Duchêne, Ali Mohammad-Djafari.
9. Variational Bayesian Approach and Bi-Model for the Reconstruction-Separation of Astrophysics Components, Thomas Rodet, Aurélia Fraysse, Hacheme Ayasso.
10. Kernel Variational Approach for Target Tracking in a Wireless Sensor Network, Hichem Snoussi, Paul Honeine, Cédric Richard.
11. Entropies and Entropic Criteria, Jean-François Bercher.

About the Authors

Jean-François Giovannelli is Professor at the University of Bordeaux in France and carried out research at the IMS laboratory into signal and image processing. His contributions concern inverse problems, deterministic and Bayesian regularization and in particular myopic and unsupervised aspects.
Jérôme Idier is CNRS Director of Research at IRCCyN in Nantes, France. He is a member of the French national committee for scientific research. His research work concerns inference and optimization for the solution of inverse problems in signal and image processing.


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