Master 2 MVA

This is the homepage for my course Sparsity and compressed sensing in Master 2 Mathématiques, Vision, Apprentissage - MVA.


This course reviews the applications of sparse representations in image processing, with an emphasis on the compressed sensing method. It alternates between the exposition of the theory and a practical implementation of the methods. Sparsity has recently emerged as a fundamental tool in image processing. It allows one to take into account the compressibility of images in a well chosen representation. It leads to state of the art methods to regularize inverse problems such as super-resolution, medical imaging and astrophysical imaging. It is also at the heart of compressed sensing, a revolutionary method to sample data in an already compressed form.


Basics of linear algebra, calculus and Fourier transform.

Validation of the course

Attending all the numerical tours, a mini-project with a report and an oral presentation. Note that there is a special session dedicated to the preparation of the projects.


List of lectures

  1. Introduction: Fourier and Wavelet analyses - Slides - Numerics: Image Approximation with Orthogonal Bases.
  2. Inverse problems and variational regularization - Slides - Numerics: Image Deconvolution using Variational Method.
  3. Sparsity and L1 regularization - Slides - Numerics: Inpainting using Sparse Regularization.
  4. Convex optimization for imaging - Slides - Numerics: Primal-Dual Proximal Splitting.
  5. Compressed Sensing - Slides - Numerics: Compressed sensing phase transition.
  6. Theoretical performance guarantees of sparse recovery - Slides - Numerics: Mini-project help desk.
  7. Mini-projects oral exam.

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