Course Overview

The course deals with methods, models and algorithms for inverse
problems in imaging. The subject matter of the course is exemplified
through a variety of application field (medical, astrophysical,
geophysical, remote-sensing, non-destructive evaluation, etc.) and
several imaging modalities (scanner, tomography, echography, optical
imaging, MRI, etc.). The core of the course deals  with problems such
as: deconvolution, Fourier synthesis, inverse Radon, denoising, etc.
The focus is on the deconvolution problem.

Learning Achievement

Competence

Course prerequisites

- Level B2 CEFR in English
- Basic knowledge of linear algebra (matrix, eigenvalue,
positive-definite matrix, etc.).

Grading Philosophy

Written examination (3 hours) and practical work.

Course schedule

- The first chapter deals with standard linear methods (inverse
filter, Wiener, shortly Kalman...) based on quadratic criteria. They
often strike an interesting compromise between the quality of the
restored images on the one hand and ease of implementation and
numerical efficiency on the other hand.
- The second chapter resorts to non-quadratic convex criteria
(differentiable or not) and the optimization step relies on
half-quadratic techniques. It allows for efficient edge-preserving
image restoration.
- The third point is devoted to constraints, mainly positivity and
support. Implementation is based on augmented Lagrangian and
Alternative Direction Methods of Multipliers (ADMM).These approaches
result in resolution improvement of computed images.
- The last point deals with unsupervised and myopic problems. They
are partially open questions, crucial in practical applications and
attractive from a theoretical standpoint. A possible solution takes
advantage of a Bayesian interpretation of the previously mentioned
scheme and allows for self-tuned and self-calibrated methods.

Course type

> Face-to-face teaching teaching (50 hours): - Lectures (20 hours), - Tutorial classes (10 hours), - Practical work (20 hours). > 100 hours personal work.

Online Course Requirement

Instructor

Other information

Duration: 12 weeks

Language of instruction: English
Mode of delivery: Face-to-face teaching; Personal work.

Site for Inquiry