logo Insalogo Insa




  • Mathematical modeling of the main image acquisition devices.
  • Image restoration : Modeling, total variation, noise reduction, inverse problems (inpainting, deconvolution, compressed image restoration).
  • Image registration: Principle and Overview of variational models in registration and applications
  • Sparse representation in a dictionary of atoms: principle, l0 and l1 minimization, compressed sensing (case l0 and l1 with the RIP criterion), Orthogonal MatchingPursuit.
  • Image segmentation: shape optimization with the levelset method of the maximum flow. Modeling for image segmentation: Mumford-Shah model, Chan-Vese, Boykov-Jolly
  • Non-local methods: Discrete Universal Denoiser, NL-mean, non-local total variation.
  • Learning methods (not convex) dictionary learning, K-SVD.


At the end of this module, the student will have understood and be able to explain (main concepts):

The image acquisition process, the basics and the use of optimization methods for solving inverses problems meet in image processing. The main applications are image restoration, segmentation and registration.


The student will be able to:

manipulate, implement and perform tests on novel image processing methods. In order to do so, the student will need to calculate the gradients, projections and proximal operators he needs to implement an algorithm adapted to structure of his problem.

Needed prerequisite

Basics in linear algebra, non-linear optimization, statistics and probability, programming

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...