Lectures - Prof. Simon Masnou
Lectures
Lecture 1
Basics of image processing: the image formation process, color images,
compression.
Classical restoration problems.
The inpainting problem: introduction and survey on variational/PDE
methods for 2D still images.
Lecture 2
Inpainting: from texture synthesis to exemplar-based inpainting methods,
connections with the PatchMatch algorithm and the Nonlocal Means
A quick survey of local and nonlocal denoising methods.
Lecture 3
Nonlocal operators for image regularization
Variational interpretation of exemplar-based methods
Dictionary-based/sparse inpainting
A few methods for 3D inpainting
Video inpainting: old and new results.
Lecture 4
The Arias-Facciolo-Caselles-Sapiro's variational model for image
regularization and inpainting: introduction, main properties, algorithms,
and experimental results.
Lecture 5
The Arias-Facciolo-Caselles-Sapiro's variational model for image
regularization and inpainting: proofs of some mathematical properties of
the model.
Lecture 6
The Sadek-Arias-Facciolo-Caselles' method for gradient domain video
editing: introduction, algorithm, experimental results.
Old movie restoration: an a-contrario model for blotch detection.
Lectures - Prof. Antonin Chambolle
Lectures
Lecture 1
Inverse problems in image reconstruction.
The advantages of the Total Variation for imaging.
The functions with bounded variation: examples, properties.
Lecture 2
Sets with finite perimeter.
Variational problems; geometric minimization problems (prescribed curvature sets).
Comparison principles, in the discrete and continuous settings.
Lecture 3
Some qualitative results for solutions (jump set, continuity, ...) and related issues.
Lecture 4
Discretization. The case of $\ell^1$ type total variation:
linear programs, second order cone programs, representation
on graphs and exact algorithms.
Lecture 5
Nonsmooth convex optimization. Rates of convergence.
Algorithms, accelerated gradient descent. Primal-dual approaches.
Extragradient ("mirror prox"), accelerated primal-dual optimization.
Examples.
Lecture 6
General scalar or vectorial total variations.
Application to (not necessarily convex) multi-labelling problems.
