MSc: Image Reconstruction

A short tour from analytical to data-driven methods

FIG: Some reconstructed images.

This course explores the mathematics and algorithms behind computational imaging systems. We focus on the "Inverse Problem"—the process of reconstructing the internal structure of an object from external physical measurements. While the curriculum uses X-ray CT and ultrasound imaging as primary case studies, these computational techniques are universal, applying to everything from medical diagnostics to industrial testing and geophysics.

Topics include:
* Physical foundations: We examine the physics of X-ray and ultrasound waves to understand the "forward model" (i.e., how measurements are performed).
* Analytical methods: We explore transform-based solutions (like the Radon transform) used for real-time reconstruction.
* Optimization-based methods: We learn how to solve ill-posed problems where measurements are noisy or incomplete. This covers the fundamentals of algebraic reconstruction, data fidelity, and regularisation.
* Data-driven methods: We explore how neural networks can increase the speed and accuracy of image reconstruction pipelines.

Lectures: PDF of the notes
Coding sessions: Python exercises
Past exams: 2026, 2025, 2024, 2023, 2022, 2021 (in French), 2020 (in French), 2019 (in French), 2018 (in French), 2017 (in French),