Master 2 - Mathématiques / Vision / Apprentissage (MVA)
Course : Sparsity and compressed sensing

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.

Pre-requisite: basics of linear algebra, calculus and Fourier transform.

Validation of the course: attending all the numerical tours (5pts/20), a mini-project with a report (5pts/20) and an oral presentation (10pts/20). 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 phrase transition
  6. Theoretical performance guarantees of sparse recovery. [Slides]
    Numerics : Mini-project help desk
  7. Mini-projects oral exam.

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