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Image and sound processing

446-1 Image and sound processing Computer Science S9
Lessons : 18 h TD : 2 h TP : 10 h Project : 0 h Total : 30 h
Co-ordinator : Jalal Fadili
Prerequisite
Image processing, introduction to optimization.
Course Objectives
The main objective of this course is to describe the main methods entering into play to solve inverse problems in image processing, with a particular focus on restoration and recovery. Concrete examples will be considered in the lab sessions.
Syllabus
Modern image processing builds on theoretical approaches of which variational, statistical and PDE-based methods are the most important. These methods are the backbone of the modern tools to solve inverse problems such as deconvolution, inpainting, computerized tomography to a name a few.

This course is divided into three main parts:
1. PDEs' on graphs and applications.
2. PDEs' for image processing.
3. Variational methods and optimization to solve inverse problems.
Practical work (TD or TP)
Restoration, reconstruction, recovery, many imaging modalities in industry.
Acquired skills
Problem formalization; Efficient and guaranteed algorithms design; Advanced mathematical methods for imaging.
Bibliography
G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences). Springer, 2nd ed., 2006.

O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, and F. Lenzen, Variational Methods in Imaging, (Applied Mathematical Sciences), Springer, 2009, Vol. 167.

A. Kirsch, An introduction to the mathematical theory of inverse problems. Springer, 2011, vol. 120.

J.-L Starck, F. Murtagh, and M.J. Fadili. Sparse Signal and Image Processing : Wavelets, Curvelets and Morphological Diversity. Cambridge University Press, Cambridge, 2010.

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