Master 2 MVA

This page contains the materials needed course “Méthodes de séparation de sources pour l’analyse de données en astrophysique” given at ENS Paris-Saclay (Master 2 MVA).

All the necessary material, slides and data are available at https://github.com/BSScourse/MVA

Slides of the courses :

Course #1 : Introduction, unsupervised source separation, statistical principles

Course #2 : Advanced Independent Component Analysis

Course #3 : Unsupervised source separation, the sparse way

Course #4 : Optimisation and proximal algorithms for source separation-take I

Course #5 : Optimisation and proximal algorithms for source separation-take II

Course #6 : Plug & play methods, applications to astrophysics

Course #7 : Non-Negative Matrix Factorisation, theory and practice

Course #8 : Advanced NMF, from linear to non-linear models

References :

Books :

Astronomical Image And Data Analysis, Starck, Murtagh, Springer

Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity, Starck, Murtagh, Fadili, Cambridge University Press

Astronomical Image And Data Analysis, Starck, Murtagh, Springer

Handbook of blind source separation, Comon, Jutten, Academic Presss

Articles :
Sparse representations

The undecimated wavelet decomposition and its reconstruction (more details about the starlet)

Curvelets and ridgelets(all about the curvelet and ridgelet transform)

The curvelet transform for image denoising

Sparse Poisson intensity estimation(wavelet, sparsity for image denoising)

Discussions about the Bayesian interpretation of sparsity :

Sparsity and the Bayesian perspective

Should penalized least squares regression be interpreted as Maximum A Posteriori estimation?

Convex optimization and proximal calculus:

Proximal algorithms

Forward-backward splitting algorithm

Accelerated first-order proximal algorithms

Primal-dual proximal algorithms

Convex analysis

Article on reweighted L1 techniques

Independent component analysis:

A Unifying Information-Theoretic Framework for Independent Component Analysis

ICA: statistical principles

Sparse blind source separation:

Sparse BSS, MMCA

Sparse BSS, GMCA

Non-negative matrix factorization:

Lee & Seung

Sparse NMF, Kim & Park

Sparse NMF, sparse domain, Rapin et al

H-ALS

Dictionary learning:

K-SVD algorithm, application to denoising

Learning the morphological diversity

Original paper by Olshausen & Fields