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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...).

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 post-processing 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 Sachs-Wolfe 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 cross-correlating 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 large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation 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 curl-free and divergence-free wavelets, which allows to better recover the information on the border of the field (Deriaz, Starck, Pires A&A,, 2012).
  • High-Order Statistics: We have shown that i) sparse representation could help to discriminate cosmological models (Pires, Starck et al, MNRAS, 2009), ii) high-order 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 non-linear 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 forward-computing model to predict peak counts from an analytical mass function input. This model will be able to take into account realistic survey-like 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, Lachieze-Rey, 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 shell-like structures in the density field, with characteristics similar to those expected from BAO (Arnalte-Mur, 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, Lachieze-Rey, ApJ,2012a) (Labatie, Starck, Lachieze-Rey, 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 multi-scale 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 multi-band optical data over 133 square degree in the CFHTLS-Wide survey, from z=0.2 to 1.2 (Coupon, Kilbinger et al., A&A, 2012). Comparing these observations to a semi-analytical model of the matter distribution in the Universe, including a prescription how galaxies populate halos, a so-called halo occupation distribution (HOD) model, we determine the evolution of the luminosity-to-mass (L/M) ratios for stellar-mass 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 “anti-hierarchical” evolution or “down-sizing”, where galaxies formed more efficiently in larger halos in the past.

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 non-negative mixtures of non-negative sources (non-negative 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 MPEGx-based 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 MJPEG-based encoder, with the efficiency of an MPEGx-based decoder, in the framework of CS. We showed that the proposed CVS system is able to achieve a high-quality 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 full-resolution data (Tzagkarakis et al, PCS, 2012), (Tzagkarakis et al, EUSIPCO, 2012).
  • Range Imaging: We have introduced a novel approach for Time-of-Flight (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 state-of-the-art 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 low-resolution 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 signal-strength values received from a set of access points. Then, these compressed measurements are employed in the framework of compressed sensing to recover a sparse position-indicator 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 state-of-the-art methods, while using a highly reduced set of data (compressed signal-strength values), thus increasing the system's lifetime (Milioris, Tzagkarakis, et al, J. of Ad Hoc Networks, 2012), (Milioris, Tzagkarakis, et al, EUSIPCO, 2011).
We have been involved in the following education activities:
Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France.