Course Overview

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.

Learning Achievement

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

Competence

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.

Course prerequisites

basic analysis and linear algebra

Grading Philosophy

Lab work report and written exam

Course schedule

Course type

Lecture

Online Course Requirement

Instructor

Laurent Condat

Other information

Course content can evolve at any time before the start of the course. It is strongly recommended to discuss with the course contact about the detailed program.

Please consider the following deadlines for inbound mobility to Grenoble:
- April 1st, 2020 for Full Year (September to June) and Fall Semester (September to January) intake ;
- September 1st, 2020 for Spring Semester intake (February – June).

Site for Inquiry