Main description:

Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation.
In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

Contents:

Part 1: Fundamental problems and tools. Chapter 1. Inverse problems, ill-posed problems (Guy Demoment, Jerome Idier). Chapter 2. Main approaches to the regularization of ill-posed problems (Guy Demoment, Jerome Idier). Chapter 3. Inversion within the probabilistic framework (Guy Demoment, Yves Goussard). Part 2: Deconvolution. Chapter 4. Inverse filtering and other linear methods (Guy Le Besnerais, Jean-Francois Giovannelli, Guy Demoment). Chapter 5. Deconvolution of spike trains (Frederic Champagnat, Yves Goussard, Stephane Gautier, Jerome Idier). Chapter 6. Deconvolution of images (Jerome Idier, Laure Blanc-Feraud). Part 3: Advanced problems and tools. Chapter 7. Gibbs-Markov image models (Jerome Idier). Chapter 8. Unsupervised problems (Xavier Descombes, Yves Goussard). Part 4: Some applications. Chapter 9. Deconvolution applied to ultrasonic non-destructive evaluation (Stephane Gautier, Frederic Champagnat, Jerome Idier). Chapter 10. Inverse problems in optical imaging through atmospheric turbulence (Laurent Mugnier, Guy Le Besnerais). Chapter 11. Spectral characterization in ultrasonic Doppler velocimetry (Jean-Francois Giovannelli, Alain Herment). Chapter 12. Tomographic reconstruction from few projections (Ali Mohammad-Djafari, Jean-Marc Dinten). Chapter 13. Diffraction tomography (Herve Carfantan, Ali Mohammad-Djafari). Chapter 14. Imaging from low-intensity data (Ken Sauer, Jean-Baptiste Thibault).