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Convex Optimisation (SIGMA S9) - WPMTIPO7

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  • Number of hours

    • Lectures : 12.0
    • Tutorials : 6.0
    • Laboratory works : 0
    • Projects : 0
    • Internship : 0
    ECTS : 2.0

Goals

The objective is to introduce the concepts of convex optimization and applications to inverse problems.

Contact Laurent CONDAT, Romain COUILLET, Ronald PHLYPO

Content

This course focuses on formulating signal and image processing problems as convex optimization problems, analyzing their properties (e.g. existence and uniqueness of solutions) and designing efficient algorithms to solve them numerically. We aim at giving students the background and skills to formulate problems and use appropriate algorithms on their own applications.
Syllabus:?* Convex optimization: existence and uniqueness of solutions, subdifferential and gradient, constraints and indicator functions, monotone inclusions, nonexpansive operators and fixed point algorithms, duality, proximal operator, splitting algorithms.?* From estimation to optimization: formulating priors and constraints, regularity and parsimony, Bayesian interpretation.

  • Inverse problems: well- and ill-posed problems, data fidelity and regularization, study of signal and image recovery problems.


Prerequisites

basic analysis and linear algebra

Tests

Semester 9 - The exam is given in english only 

Lab work report * 40% + written exam * 60%



Devoir surveille * 60% + Compte rendu TP * 40%

Additional Information

Semester 9 - This course is given in english only EN

Curriculum->Master TSI SIGMA->Semester 9
Curriculum->Double-Diploma SICOM-TSI SIGMA->Semester 9
Curriculum->Master->Semester 9
Curriculum->Double-Diploma Engineer/Master->Semester 9

Bibliography

H. H. Bauschke and P. L. Combettes, « Convex Analysis and Monotone Operator Theory in Hilbert Spaces », 2011
N. Parikh and S. Boyd, « Proximal Algorithms », Foundations and Trends in Optimization Vol. 1, No. 3 (2013) 123–231
P. L. Combettes and J.-C. Pesquet, « Proximal splitting methods in Signal Processing », chapitre de « Fixed-point algorithms for inverse problems in science and engineering », p. 185-212, 2011.

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Date of update January 9, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes