Authors

Nelly Pustelnik - nelly.pustelnik@ens-lyon.fr

Audrey Repetti - A.Repetti@hw.ac.uk

Summary

Image processing aims to extract or interpret the information contained in the observed data linked to one (or more) image(s). Most of the analysis tools are based on the formulation of an objective function and the development of suitable optimization methods. This class of approaches, qualified as variational, has become the state-of-the-art for many image processing modalities, thanks to their ability to deal with large-scale problems, their versatility allowing them to be adapted to different contexts, as well as the associated theoretical results ensuring convergence towards a solution of the finite objective function.

Slides of the course

1- Inverse problems and variational approaches - pdf

2- Variational approaches: From inverse problems to segmentation - pdf

3- Variational approaches in supervised learning - pdf

4- Optimisation algorithms - pdf

5- Optimisation algorithms: Block-coordinate approaches - pdf

6- Supervised learning for solving inverse problems - pdf

Python notebook

1- Play with direct model - Notebook

2- Image deconvolution considering Forward-Backward algorithm, FISTA and Condat-Vu algorithm - Notebook

3- Image denoising and deconvolution with Plug-and-Play Forward-Backward - Notebook

Required packages :

• numpy

• matplotlib

• PIL

• scipy

• pywt

• bm3d

• torch

• numba

• pylobs

• jupyter

Informations

This course has been created for “Journées SMAI-MODE 2022, Limoges”

Affiliations and websites of the authors

Nelly Pustelnik: CNRS, Laboratoire de Physique, ENS de Lyon, France and INMA, UCLouvain, Belgium

Audrey Repetti : Heriot-Watt University, Maxwell Institute, Edinburgh, UK