
CosmoStat Laboratory


CosmoStat is a laboratory of AIM
at CEA/IRFU.
The scientific field of the CosmoStat
interdisciplinary entity is Computational
Cosmology. CosmoStat goals are:
 Statistics & Signal Processing:
Develop new methods for analyzing
astronomical data, and especially in
cosmology (PLANCK, EUCLID, etc) where
the needs of powerful statistical
methods are very important.
 Cosmology: Analyze and interpret data.
 Projects: Participation to important
astronomical projects: PLANCK, FERMI,
HERSCHEL, EUCLID, etc.
 Teaching: Teach students and young
researchers how to analyze astronomical
data.
 Dissemination: Take opportunity to
disseminate our idea and tools in and
outside the astronomical field (CEA,
CNRS, University, Industry...).

RECENT NEWS


RESEARCH IN
COSMOLOGY

Cosmic Microwave Background
(CMB):
We have been working on several aspects
relative to CMB data:
 CMB map reconstruction:
We solve the problem of CMB map
reconstruction from multichannel
observations obtained by instruments,
such as WMAP or PLANCK. We have shown
that our sparse component separation,
called GMCA, can be used to recover both
CMB and SZ maps
(Bobin et al, Astronomy and
Astrophysics, 2013). We have also
shown that a postprocessing using
sparse representation could be very
useful for noise and foreground removal
(Bobin, Starck, Sureau, Fadili,
A&A, 2012).
 Sparse Representation of
Polarized Spherical Data: We
have developed new decompositions
(wavelet and curvelet) on the sphere for
polarized data (Starck
et al, A&A, 2009;
Paykari and Starck, A&A, 2012).
The software SparsePol (Polarized
Spherical Wavelets and Curvelets) has
been developed, documented, and is
available since June 2010 at:
http://jstarck.free.fr/mrsp.html .
 Integrated SachsWolfe
effect detection (ISW): ISW
detection consists in detecting a very
weak signature of the matter in the CMB,
due to the passage of CMB photons
through the gravitational potential.
This is done by crosscorrelating a
galactic survey, which traces the matter
and a CMB map. We have proposed a new
method to make this detection, based on
sparse representations in order to take
into account missing values and a
parametric bootstrap techniques allowing
us to properly estimate the detection
level. This method has been applied on
WMAP and 2MASS (Dupe,
Rassat, Starck, A&A, 2012).
Our results (2sigma detection) is
compatible with the expected signal in
the standard cosmological model, and do
not confirm high detection levels (>
4sigma) claimed by few other groups.
 Sparse recovery of the Primordial Power Spectrum: The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the largescale structure we observe today, and thereby provides an indirect probe of inflation or other structureformation mechanisms. We have developed PRISM, a sparsity based inversion algorithm allowing us to reconstruct from CMB measurements the global shape of the Primordial Power Spectrum as well as isolated features. We have applied this technique on both WMAP9 (Paykari et al., A&A, 2014) and Planck data (Lanusse et al., A&A, 2014) and we find no significant departure from the Planck PR1 best fit power law.
Weak Lensing:
 2D Convergence Mass Map: We
have applied to the COSMOS data our mass
map reconstruction method and we have
shown a good spatial correlation between
visible and dark matter (Massey
et al, Naturex, 2007; Pires,
Starck and A. Refregier, IEEE Signal
Processing Magazine, 2010). We
have also shown that there is a clear
relation between the Helmholtz
decomposition of a vector field and the
E and B modes reconstruction from weak
lensing data, and we have derived a new
Wavelet Helmholtz decomposition to
reconstruct the dark matter mass map.
Using this idea, we can design very
specific curlfree and divergencefree
wavelets, which allows to better recover
the information on the border of the
field (Deriaz,
Starck, Pires A&A,, 2012).
 HighOrder Statistics: We
have shown that i) sparse representation
could help to discriminate cosmological
models (Pires,
Starck et al, MNRAS, 2009), ii)
highorder statistics should be
performed on the wavelet decomposition
of the convergence map rather than on
the aperture mass map (Leonard,
Pires, Starck, MNRAS, 2012), and
iii) that the best cosmological
constraint are obtained using a wavelet
peak counting statistic on the sparse
denoised convergence map (Pires,
Starck, et al, MNRAS, 2012).
 3D Density Mass: We
have worked on the extension of the weak
lensing reconstruction operator to the
third dimension (i.e. tomographic weak
lensing), and we have found a very
interesting behavior of this operator.
It acts in fact as a Compressed Sensing
operator (i.e. it spreads out any
localized information over all
measurements). Then l1 sparse recovery
is an interesting approach to
reconstruct the 3D mass distribution. We
have shown that sparse nonlinear methods offer a very promising way of reconstructing the 3D density mass maps that outperforms significantly all
existing methods
(Leonard, Dupe, Starck, Fadili,
A&A, 2012b). In particular, we
have seen using simulations that we can
reconstruct two clusters on the same
light of sight, which was impossible
with previous methods. Extending this work, we introduced a new sparse reconstruction technique, called GLIMPSE, and have showed on simulations that this method is able to reconstruct both the density and redshift of dark matter halos with enough accuracy to put constraints on the halo masses (Leonard, Lanusse, Starck, A&A, 2014).
 Peak counting:
Weak lensing peaks are tracers of high mass regions. They provide a way to probe the mass function and to study cosmology.
We are developping a forwardcomputing model to predict peak counts from an analytical mass function input.
This model will be able to take into account realistic surveylike conditions.
Spatial Distribution of Galaxies:
 Two point correlation
function (2PCF): We have
investigated whether Labini's group
claim, that the 2PCF at large scales
behavior in galaxy surveys (BAO,
Universe homogenization) cannot be
trusted due to the limited volume
effect, is correct. We have demonstrated
that all 2PCF estimators verifies a
relation called integral constraint,
which is not necessary by the real 2PCF,
which biases correlation function
estimators. But we showed using
simulations of the Sloan Digital Sky
Survey Data Release 7 (SDSS DR7) that
the effect of the constraint is very
small for current galaxy surveys (Labatie,
Starck, LachiezeRey, Statistical
Methodology, 2011).
 Baryonic Acoustic
Oscillation (BAO): We have
designed a specific wavelet adapted to
search for shells, and exploit the
physics of the process by making use of
two different mass tracers, introducing
a specific statistic to detect the BAO
features. We have applied our method to
the detection of BAO in a galaxy sample
drawn from the Sloan Digital Sky Survey
(SDSS). We have used the "main"
catalogue to trace the shells, and the
luminous red galaxies (LRG) as tracers
of the high density central regions.
Using this new method, we detect, with a
high significance, that the LRG in our
sample are preferentially located close
to the centers of shelllike structures
in the density field, with
characteristics similar to those
expected from BAO (ArnalteMur,
Labatie, Clerc, Martínez,
Starck et al, A&A, 2012).
Then we have studied the classical
method for detecting BAOs and the
assumptions that the method requires. We
have also found that the approximation
of a constant covariance matrix in the
classical BAO analysis method can affect
non negligibly both the BAO detection
and cosmological parameter constraints (Labatie,
Starck, LachiezeRey, ApJ,2012a)
(Labatie, Starck, LachiezeRey,
ApJ,2012b).
 Multiscale morphology of
the galaxy distribution: We
have shown how to calculate the
Minkowski Functionals (MFs) taking into
account border effects of complex
observational sample volumes. We have
proposed a multiscale extension of the
MF, which gives us more information
about how the galaxies are spatially
distributed. This method has been
applied to the 2dF Galaxy Redshift
Survey data. The MMF clearly indicates
an evolution of morphology with scale.
We also compare the 2dF real catalogue
with mock catalogues and found that Λ
cold dark matter simulations roughly fit
the data, except at the finest scale
(Saar, Martinez, Starck and Donoho,
MNRAS, 2007).
 Galaxy clustering and the
changing relationship between galaxies
and haloes since z=1.2: We
measured the galaxy spatial correlation
function in multiband optical data over
133 square degree in the CFHTLSWide
survey, from z=0.2 to 1.2
(Coupon, Kilbinger et
al., A&A, 2012).
Comparing these observations to a
semianalytical model of the matter
distribution in the Universe, including
a prescription how galaxies populate
halos, a socalled halo occupation
distribution (HOD) model, we determine
the evolution of the luminositytomass
(L/M) ratios for stellarmass selected
galaxy samples. A maximum L/M is reached
at halo masses of 6.3 × 1011 at low
redshift. This mass increases with
redshift, indicating “antihierarchical”
evolution or “downsizing”, where
galaxies formed more efficiently in
larger halos in the past.


RESEARCH IN
SIGNAL PROCESSING/STATISTICS

Sparse Representation of
Signals:
A signal is said to be sparse if it can be
represented in a basis or frame (Fourier,
Wavelets, Curvelets, etc.) in which the
curve obtained by plotting the obtained
coefficients, sorted by their decreasing
absolute values, exhibits a polynomial
decay. The basis or frame is called the
dictionary. Note that most natural signals
and images are compressible in an
appropriate dictionary. Faster is the decay,
better it is, since a very good
approximation of the signal can be obtained
from a few coefficients. For instance, for a
signal composed of a sine, the Fourier
dictionary is optimal from a sparse point of
view since all information is contained in a
single coefficient. Wavelets have been
extremely successful to represent images,
most natural images present a sparse
behavior in the wavelet domain, and this
explains why wavelets have been chosen in
the JPG2000 image compression norm. Other
representations, such as curvelets, are more
adequate when the data contains filaments.
We have been working on several ill posed
inverse problems where we have shown that
sparsity is a very efficient way to
regularize the problem in order to get a
unique and stable solution
(Starck et al, Cambridge University Press,
book, 2010):
 Blind Source Separation
(BSS): Exceptional results
were obtained (Bobin,
Starck et al, IEEE Trans. on Image
Processing, 2007),
(Bobin, Starck, et al, Journal of
Mathematical Imaging and Vision, 2009)
when sparsity is used to recover sources
from a set of multichannel observations,
each channel containing a mixture of the
different sources (classic BSS problem).
This framework was also extended so as to deal
with nonnegative mixtures of nonnegative sources
(nonnegative matrix factorization, NMF,
Rapin, Bobin, Larue, Starck, IEEE Transactions on
Signal Processing, 2013 and
Rapin, Bobin, Larue, Starck, SIAM Journal
on Imaging Sciences, 2014).
An overview of our activities in BSS can
be found at this
location, which includes code samples.
 Inpainting: we
have shown that missing data could be
interpolated in very efficient way using
sparsity (Fadili,
Starck, Murtagh, Computer Journal,
2009).
 Deconvolution: We
have studied the recent proximal theory
in optimization theory, and shown that
it provides very elegant solutions for
image restoration (Dupé,
Starck, et al, IEEE Trans. on Image
Processing, 2009).
 Structured Sparsity: Using
a sparse representation, such as wavelet
or curvelet decomposition, there are
some correlations between neighboring
pixels that can be captured and used to
improve denoising results. (Chesneau,
Fadili, and Starck, Applied and
Computational Harmonic Analysis, 2010).
 3D Sparse Representations:
We have extended to the third
dimension recent sparse 2D
decompositions, such as ridgelet or
curvelet (Woiselle,
Starck and Fadili, Applied and
Computational Harmonic Analysis, 2010),
(Woiselle,
Starck, Fadili, J. of Mathematical
Imaging and Vision, 2011).
 Compressed Sensing (CS): CS
is a theory which links the data
acquisition principle to the sparsity
concept. We have investigated how this
kind of new idea could be useful for the
transfer of astronomical data from
satellite, such as Herschel (Bobin,
Starck, and R. Ottensamer, IEEE
Journal of Selected Topics in Signal
Processing, 2008), and we have
developed algorithms to recover the
solution from compressed sensing data
(Donoho, Tsaig, Drori, Starck, IEEE
Transactions on Information Theory,
2012). We have shown using a
Herschel data set, especially acquired
to test the CS approach, that CS could
indeed be a very practical solution for
astronomical data transfer from a
satellite to earth (Barbey,
Sauvage, Starck, Ottensamer, A&A,
2011).
 Compressive Video Sensing
(CVS): We tackled the
problem of designing efficient codecs
for lightweight remote imaging systems
by embedding compressed sensing in
already existing video compression
standards. First, we modified an
MPEGxbased imaging system and we showed
that our proposed CVS method achieves a
comparable, or an even superior,
performance when compared with MPEGx,
but at significantly reduced bit rates,
especially for noisy videos. Then, in
order to satisfy the limited power,
memory, and bandwidth resources of a
lightweight remote imaging system, we
combined the simplicity of an
MJPEGbased encoder, with the efficiency
of an MPEGxbased decoder, in the
framework of CS. We showed that the
proposed CVS system is able to achieve a
highquality reconstruction at even
lower bit rates, with this reduction in
the necessary bit rate to increase by
introducing an efficient compressed
measurements allocation scheme (Tzagkarakis,
Woiselle, Tsakalides, Starck, VISAPP,
2012). Moreover, we developed
algorithms for the classification of
video sequences by exploiting directly
the highly reduced set of compressed
measurements. The proposed techniques
improved the classification accuracy of
previous commonly used classifiers,
without requiring access to the original
fullresolution data (Tzagkarakis
et al, PCS, 2012), (Tzagkarakis
et al, EUSIPCO, 2012).
 Range Imaging:
We have introduced a novel approach for
TimeofFlight (ToF)based range
imaging, which utilizes the recently
introduced theory of compressed sensing
to dramatically reduce the number of
necessary frames required for the
reconstruction of a depth map. Our
technique employs a random gating
function along with stateoftheart
minimization techniques in order to
estimate the location of a returning
laser pulse and subsequently to infer
the distance. Our experimental results
have shown that sampling rates at the
order of 20% of the frames that
traditional ToF cameras require, can
achieve almost perfect reconstruction in
lowresolution regimes, while the
proposed method is also robust to
realistic noise models (Tsagkatakis,
Woiselle, Tzagkarakis, Bousquet,
Starck, Tsakalides, SPIE
Security+Defence, 2012).
 Wireless Sensor Networks
(WSN): We have shown that
accurate joint reconstruction of a
sparse signal ensemble can be achieved
in a decentralized fashion, by
exchanging a minimum amount of
information among the sensors of a WSN.
The reconstruction is performed by
developing a novel distributed Bayesian
Matching Pursuit algorithm, which was
shown to be superior in terms of
reconstruction accuracy, when compared
with previous centralized approaches,
while employing a small number of random
incoherent projections, thus satisfying
potential resource constraints (Tzagkarakis,
Starck, Tsakalides, EUSIPCO, 2011).
In addition, motivated by the recent
wide use of wireless networks in the
application of estimating the position
of a mobile user, we developed efficient
localization algorithms by working
directly with a compressed set of
signalstrength values received from a
set of access points. Then, these
compressed measurements are employed in
the framework of compressed sensing to
recover a sparse positionindicator
vector. Our proposed approach, which is
also shown to be very robust in noisy
environments, results in a significant
improvement of the localization accuracy
when compared with previous
stateoftheart methods, while using a
highly reduced set of data (compressed
signalstrength values), thus increasing
the system's lifetime
(Milioris, Tzagkarakis, et al, J. of
Ad Hoc Networks, 2012), (Milioris,
Tzagkarakis, et al, EUSIPCO, 2011).


TEACHING

We have been involved in the following
education activities:


CONTACT ADDRESS

Service d'Astrophysique,
CEASaclay, 91191 GifsurYvette, France.






