This page contains the materials needed course “Sparsity and astrophysical data analysis” given at ENS Cachan (Master 2 MVA).
Slides of the courses :
Course #1 : Introduction to astrophysical data analysis slides 1 slides 2
Course #2 : Multiresolution analysis, wavelets and beyond slides
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
Practical work :
We strongly advise the use of either Matlab or Python for these practical works.
Usually, part of the practical works are done during the course; we strongly advise to bring your laptop with you !
Participants that opt for Python will find the following modules helpful:
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–ipython
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–scipy/numpy
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–matplotlib
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–scikit-learn
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–pyfits.
- -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, 13th 2019
necessary material: ngc2997.fits , ngc2997.mat and codes to read FITS files in Matlab
some codes (numerical part of the solution): codes
PW #2 : Sparsity and its application to linear inverse problems
Report expected for february, 27th 2019
necessary material: data
some codes (numerical part of the solution):
PW #3 :Blind source separation
Report expected for march, 13th 2019
necessary material: data and codes
Mini-projects :
Report expected for april 1st, 2019
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:
Forward-backward splitting algorithm
Accelerated first-order proximal algorithms
Primal-dual proximal algorithms
Article on reweighted L1 techniques
Independent component analysis:
A Unifying Information-Theoretic Framework for Independent Component Analysis
Sparse blind source separation:
Non-negative matrix factorization:
Sparse NMF, sparse domain, Rapin et al
Dictionary learning:
K-SVD algorithm, application to denoising