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Accueil > Formations > Master MVA > Présentation des cours
Optimization and features of optimal solutions. Applications in imaging.
Intervenant : Mila Nikolova - cours théorique (CMLA (CNRS-UMR 8536)-ENS de Cachan) et Saïd Ladjal - travaux pratiques (TP) sur ordinateur (Télécom ParisTech)
Course Objective :
Understanding the practical and theoretical aspects of optimization models and methods.
Course Outline :
What is Optimization? Optimization problems in imaging sciences.
Fine properties of optimal solutions and objective functions.
- Smooth/nonsmooth problems. (What is sparsity?)
- Convex/nonconvex problems. (How to get sharp edges?)
- Combining data-fidelity and priors. (Some open questions.)
- Iterative algorithms
- Unconstrained Minimization
- Constrained Minimization
- Lagrange Multipliers
- Duality
Organization of courses :
- 5 lectures of 3 hours
- 5 lab work sessions of 3 hours
Assessment scheme
- Lab work marks
- Project mark
- Final grade: combination of the above
Textbooks :
- P. G. Ciarlet, Introduction to Numerical Linear Algebra and Optimization, Cambridge University Press 1989, Dunod, Paris, 5th ed. 2000
- H. Bauschke, P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, 2011
- O. Scherzer (Ed.) Handbook of Mathematical Methods in Imaging, Springer 1st ed. 2011, 2nd ed. 2015
Contact
M. Nikolova - nikolova@cmla.ens-cachan.fr
S. Ladjal - ladjal@enst.fr
http://mnikolova.perso.math.cnrs.fr/Optim_M2.pdf
http://mnikolova.perso.math.cnrs.fr/Optim_M2_minimizers.pdf