Bayesian Approach to Inverse Problems

Bayesian Approach to Inverse Problems

Edited by

Jérôme Idier, IRCCyN, Nantes, France

ISBN : 9781848210325

Publication Date : April 2008

Hardcover 384 pp

190 USD



The goal of this book is to deal with inverse problems and regularized solutions using Bayesian statistical tools, with a particular view to signal and image estimation.

Chapters 1-3 cover the theoretical notions that make it possible to cast inverse problems within a mathematical framework. Chapters 4-6 address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. Chapters 9-14 put the main tools introduced in the previous chapters into a practical context in important applicative areas, such as astronomy or medical imaging.


Part 1. Fundamental Problems and Tools
1. Inverse Problems, Ill-posed Problems, Guy Demoment, Jérôme Idier.
2. Main Approaches to the Regularization of Ill-posed Problems, Guy Demoment, Jérôme Idier.
3. Inversion within the Probabilistic Framework, Guy Demoment, Yves Goussard.
Part 2. Deconvolution
4. Inverse Filtering and other Linear Methods, Guy Le Besnerais, Jean-François Giovannelli, Guy Demoment.
5. Deconvolution of Spike Trains, Frédéric Champagnat, Yves Goussard, Stéphane Gautier, Jérôme Idier.
6. Deconvolution of Images, Jérôme Idier, Laure Blanc-Féraud.
Part 3. Advanced Problems and Tools
7. Gibbs-Markov Image Models, Jérôme Idier.
8. Unsupervised Problems, Xavier Descombes, Yves Goussard.
Part 4. Some Applications
9. Deconvolution Applied to Ultrasonic Non-destructive Evaluation, Stéphane Gautier, Frédéric Champagnat, Jérôme Idier.
10. Inversion in Optical Imaging Through Atmospheric Turbulence, Laurent Mugnier, Guy Le Besnerais, Serge Meimon.
11. Spectral Characterization in Ultrasonic Doppler Velocimetry, Jean-François Giovannelli, Alain Herment.
12. Tomographic Reconstruction from Few Projections, Ali Mohammad-Djafari, Jean-Marc Dinten.
13. Diffraction Tomography, Hervé Carfantan, Ali Mohammad-Djafari.
14. Imaging from Low-intensity Data, Ken Sauer, Jean-Baptiste Thibault.

About the authors

Jérôme Idier is a researcher at IRCCyN (Institut de Recherches en Cybernetique de Nantes), France.