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