A first objective of this class is to present variational approaches and partial differential equations in image processing. Students will learn to model mathematically image processing problems. The students are given the basis in order to be able to adapt classical variational models and PDEs to situations they might encounter in their future professional life.
A second objective of this class is to introduce some basics of optimization. Thanks to the first part of the course, the students can propose mathematically sounded criterion to minimize. They then need to be able to efficiently tackle them, which is the second objective of this course.
Pratical labs will illustrate the theoretical principles developed in the course.
Plan of the course:
1) PDEs in image processing (convolution, heat equation, nonlinear PDEs).
2) Variational methods in image processing (Tychnonov regularization, nonlinear regularization, functions with bounded variations, the direct method of the calculus of variations)
3) Optimization (convex functions, Euler equation, smooth optimization, nonsmooth optimization)