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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.)
Numerical methods
  • 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