Master 2 MVA

This page contains the materials needed course “Sparsity and astrophysical data analysis” given at ENS Cachan (Master 2 MVA).

Slides of the courses :

All courses will be available in early 2017

Course #1 : Introduction to astrophysical data analysis slides 1 slides 2 notebook

Course #2 : Multiresolution analysis, wavelets and beyond slides notebook

Course #3 : Inverse problems (I) slides

Course #4 : Inverse problems (II) slides

Course #5 : Applications to astrophysics slides 1  slides 2

Course #6 : Blind source separation, an introduction slides

Course #7 : Sparsity and blind source separation slides 1  slides 2

Course #8 : BSS, Non-negative matrix factorization and applications slides

Practical work :

We strongly advise the use of either Matlab or Python for these practical works.

Participants that opt for Python will find the following modules helpful:

  1. ipython

  2. scipy/numpy

  3. matplotlib

  4. scikit-learn

  5. pyfits.

  6. -pywavelets

Most of them can be set up with easily using standard porting tools (apt-get, macport … etc).

PW #1 :The starlet transform

Report expected for february, 6th 2017
necessary material: ngc2997.fits , ngc2997.mat and codes to read FITS files in Matlab

some codes (numerical part of the solution): starlet_transform

PW #2 : Sparsity and its application to linear inverse problems

Report expected for march, 2nd 2017
necessary material: data

some codes (numerical part of the solution): PW2

PW #3 :Blind source separation

Report expected for march, 30th 2017
necessary material: data and codes

Mini-projects :

Report expected for April 6th, 2017

Project #1: CMB recovery from the Planck data – description

data  – input data (for comparison purposes)

Project #2: Source separation in a radio-interferometric context  – description

data  – input data (for comparison purposes)

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