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, Nonnegative 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:

–ipython

–scipy/numpy

–matplotlib

–scikitlearn

–pyfits.
 pywavelets
Most of them can be set up with easily using standard porting tools (aptget, 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
Miniprojects :
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 radiointerferometric 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:
Forwardbackward splitting algorithm
Accelerated firstorder proximal algorithms
Primaldual proximal algorithms
Article on reweighted L1 techniques
Independent component analysis:
A Unifying InformationTheoretic Framework for Independent Component Analysis
Sparse blind source separation:
Nonnegative matrix factorization:
Sparse NMF, sparse domain, Rapin et al
Dictionary learning:
KSVD algorithm, application to denoising