Teaching

These are lecture notes from courses I teach at CentraleSupélec, IMT Atlantique, and ISEN Brest. They cover the foundations and modern methods of medical image reconstruction, with a particular focus on CT and PET.

Image reconstruction

1. Introduction to CT imaging

An introduction to X-ray computed tomography (CT), from the Beer–Lambert law and the Radon transform to the history and principles of modern CT scanners.

Language: French

2. Analytical CT reconstruction

Mathematical foundations of analytical CT reconstruction, including the Radon transform, backprojection, analytical inversion, stability, and regularisation.

Language: French

3. Iterative CT reconstruction

Introduction to discrete CT imaging models and iterative reconstruction, with an emphasis on optimisation methods for solving the resulting inverse problem.

Language: French

4. Statistical CT reconstruction

Statistical modelling of CT measurements, from Poisson photon counting and maximum-likelihood estimation to penalised reconstruction and regularisation.

Language: French

5. Statistical PET reconstruction

An introduction to positron emission tomography (PET) and statistical PET reconstruction, including Poisson models, maximum likelihood, the EM algorithm, and penalised reconstruction.

Language: French

6. Compressive sensing and non-smooth optimization for image reconstruction

Sparse and total-variation regularised image reconstruction, with an introduction to non-smooth convex optimization, proximal-gradient, primal-dual, and ADMM algorithms.

Language: French

7. Unsupervised learning for image reconstruction

Generative models as learned priors for image reconstruction, covering unsupervised learning, variational autoencoders, generative adversarial networks, and diffusion models.

Language: French