arXiv subjects

J. -L. Starck

Publications and source records attributed to J. -L. Starck.

At least 55 records · Page 3Linked to original sources

arXiv2013

Sparsity and the Bayesian Perspective

Sparsity has been recently introduced in cosmology for weak-lensing and CMB data analysis for different applications such as denoising, component separation or inpainting (i.e. filling the missing data or the mask). Although it gives very nice numerical results, CMB sparse inpainting has been severely criticized by top researchers in cosmology, based on arguments derived from a Bayesian perspective. Trying to understand their point of view, we realize that interpreting a regularization penalty term as a prior in a Bayesian framework can lead to erroneous conclusions. This paper is by no means against the Bayesian approach, which has proven to be very useful for many applications, but warns about a Bayesian-only interpretation in data analysis, which can be misleading in some cases.

astro-ph.IM↗

arXiv2013

The Scale of the Problem : Recovering Images of Reionization with GMCA

The accurate and precise removal of 21-cm foregrounds from Epoch of Reionization redshifted 21-cm emission data is essential if we are to gain insight into an unexplored cosmological era. We apply a non-parametric technique, Generalized Morphological Component Analysis or GMCA, to simulated LOFAR-EoR data and show that it has the ability to clean the foregrounds with high accuracy. We recover the 21-cm 1D, 2D and 3D power spectra with high accuracy across an impressive range of frequencies and scales. We show that GMCA preserves the 21-cm phase information, especially when the smallest spatial scale data is discarded. While it has been shown that LOFAR-EoR image recovery is theoretically possible using image smoothing, we add that wavelet decomposition is an efficient way of recovering 21-cm signal maps to the same or greater order of accuracy with more flexibility. By comparing the GMCA output residual maps (equal to the noise, 21-cm signal and any foreground fitting errors) with the 21-cm maps at one frequency and discarding the smaller wavelet scale information, we find a correlation coefficient of 0.689, compared to 0.588 for the equivalently smoothed image. Considering only the central 50% of the maps, these coefficients improve to 0.905 and 0.605 respectively and we conclude that wavelet decomposition is a significantly more powerful method to denoise reconstructed 21-cm maps than smoothing.

astro-ph.CO↗

arXiv2012

Effect of model-dependent covariance matrix for studying Baryon Acoustic Oscillations

Large-scale structures in the Universe are a powerful tool to test cosmological models and constrain cosmological parameters. A particular feature of interest comes from Baryon Acoustic Oscillations (BAOs), which are sound waves traveling in the hot plasma of the early Universe that stopped at the recombination time. This feature can be observed as a localized bump in the correlation function at the scale of the sound horizon $r_s$. As such, it provides a standard ruler and a lot of constraining power in the correlation function analysis of galaxy surveys. Moreover the detection of BAOs at the expected scale gives a strong support to cosmological models. Both of these studies (BAO detection and parameter constraints) rely on a statistical modeling of the measured correlation function $\hatξ$. Usually $\hatξ$ is assumed to be gaussian, with a mean $ξ_θ$ depending on the cosmological model and a covariance matrix $C$ generally approximated as a constant (i.e. independent of the model). In this article we study whether a realistic model-dependent $C_θ$ changes the results of cosmological parameter constraints compared to the approximation of a constant covariance matrix $C$. For this purpose, we use a new procedure to generate lognormal realizations of the Luminous Red Galaxies sample of the Sloan Digital Sky Survey Data Release 7 to obtain a model-dependent $C_θ$ in a reasonable time. The approximation of $C_θ$ as a constant creates small changes in the cosmological parameter constraints on our sample. We quantify this modeling error using a lot of simulations and find that it only has a marginal influence on cosmological parameter constraints for current and next-generation galaxy surveys. It can be approximately taken into account by extending the $1σ$ intervals by a factor $\approx 1.3$.

astro-ph.CO↗

arXiv2012

Low-l CMB Analysis and Inpainting

Reconstruction of the CMB in the Galactic plane is extremely difficult due to the dominant foreground emissions such as Dust, Free-Free or Synchrotron. For cosmological studies, the standard approach consists in masking this area where the reconstruction is not good enough. This leads to difficulties for the statistical analysis of the CMB map, especially at very large scales (to study for e.g., the low quadrupole, ISW, axis of evil, etc). We investigate in this paper how well some inpainting techniques can recover the low-$\ell$ spherical harmonic coefficients. We introduce three new inpainting techniques based on three different kinds of priors: sparsity, energy and isotropy, and we compare them. We show that two of them, sparsity and energy priors, can lead to extremely high quality reconstruction, within 1% of the cosmic variance for a mask with Fsky larger than 80%.

astro-ph.CO↗

arXiv2012

A Comparison of Algorithms for the Construction of SZ Cluster Catalogues

We evaluate the construction methodology of an all-sky catalogue of galaxy clusters detected through the Sunyaev-Zel'dovich (SZ) effect. We perform an extensive comparison of twelve algorithms applied to the same detailed simulations of the millimeter and submillimeter sky based on a Planck-like case. We present the results of this "SZ Challenge" in terms of catalogue completeness, purity, astrometric and photometric reconstruction. Our results provide a comparison of a representative sample of SZ detection algorithms and highlight important issues in their application. In our study case, we show that the exact expected number of clusters remains uncertain (about a thousand cluster candidates at |b|> 20 deg with 90% purity) and that it depends on the SZ model and on the detailed sky simulations, and on algorithmic implementation of the detection methods. We also estimate the astrometric precision of the cluster candidates which is found of the order of ~2 arcmins on average, and the photometric uncertainty of order ~30%, depending on flux.

astro-ph.CO↗

arXiv2012

A hybrid approach to CMB lensing reconstruction on all-sky intensity maps

Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous noise. For l < 100, we show that a full-sky inpainting method, already described in a previous work, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte-Carlo method, but that does not couple to the deflection field. For l>100 we develop a method based on tiling the cut-sky with local 10x10 degrees overlapping tangent planes (referred to in the following as "patches"). It requires to solve various issues concerning their size/position, non-periodic boundaries and irregularly sampled data after the sphere-to-plane projection. We show how the leading noise term of the quadratic lensing estimator applied onto an apodized patch can still be taken directly from the data. To not loose spatial accuracy, we developed a tool that allows the fast determination of the complex Fourier series coefficients from a bi-dimensional irregularly sampled dataset, without performing an interpolation. We show that the multi-patch approach allows the lensing power spectrum reconstruction with a very small bias, thanks to avoiding the galactic mask and lowering the noise inhomogeneities, while still having almost a minimal variance. The data quality can be assessed at each stage and simple bi-dimensional spectra build, which allows the control of local systematic errors.

astro-ph.CO↗

arXiv2012

Sparse component separation for accurate CMB map estimation

The Cosmological Microwave Background (CMB) is of premier importance for the cosmologists to study the birth of our universe. Unfortunately, most CMB experiments such as COBE, WMAP or Planck do not provide a direct measure of the cosmological signal; CMB is mixed up with galactic foregrounds and point sources. For the sake of scientific exploitation, measuring the CMB requires extracting several different astrophysical components (CMB, Sunyaev-Zel'dovich clusters, galactic dust) form multi-wavelength observations. Mathematically speaking, the problem of disentangling the CMB map from the galactic foregrounds amounts to a component or source separation problem. In the field of CMB studies, a very large range of source separation methods have been applied which all differ from each other in the way they model the data and the criteria they rely on to separate components. Two main difficulties are i) the instrument's beam varies across frequencies and ii) the emission laws of most astrophysical components vary across pixels. This paper aims at introducing a very accurate modeling of CMB data, based on sparsity, accounting for beams variability across frequencies as well as spatial variations of the components' spectral characteristics. Based on this new sparse modeling of the data, a sparsity-based component separation method coined Local-Generalized Morphological Component Analysis (L-GMCA) is described. Extensive numerical experiments have been carried out with simulated Planck data. These experiments show the high efficiency of the proposed component separation methods to estimate a clean CMB map with a very low foreground contamination, which makes L-GMCA of prime interest for CMB studies.

astro-ph.CO↗

arXiv2012

Wavelet analysis of baryon acoustic structures in the galaxy distribution

Baryon Acoustic Oscillations (BAO) are a feature imprinted in the density field by acoustic waves travelling in the plasma of the early universe. Their fixed scale can be used as a standard ruler to study the geometry of the universe. BAO have been previously detected using correlation functions and power spectra of the galaxy distribution. In this work, we present a new method for the detection of the real-space structures associated with this feature. These baryon acoustic structures are spherical shells with a relatively small density contrast, surrounding high density central regions. We design a specific wavelet adapted to the 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 show the effect of the BAO signal in this new statistic when applied to the Lambda - Cold Dark Matter (LCDM) model, using an analytical approximation to the transfer function. We confirm the reliability and stability of our method by using cosmological N-body simulations from the MareNostrum Institut de Ciències de l'Espai (MICE). We apply our method to the detection of BAO in a galaxy sample drawn from the Sloan Digital Sky Survey (SDSS). We use 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 LRGs in our sample are preferentially located close to the centres of shell-like structures in the density field, with characteristics similar to those expected from BAOs. We show that stacking selected shells, we can find their characteristic density profile. We have delineated a new feature of the cosmic web, the BAO shells. As these are real spatial structures, the BAO phenomenon can be studied in detail by examining those shells.

astro-ph.CO↗

arXiv2012

3DEX: a code for fast spherical Fourier-Bessel decomposition of 3D surveys

High-precision cosmology requires the analysis of large-scale surveys in 3D spherical coordinates, i.e. spherical Fourier-Bessel decomposition. Current methods are insufficient for future data-sets from wide-field cosmology surveys. The aim of this paper is to present a public code for fast spherical Fourier-Bessel decomposition that can be applied to cosmological data or 3D data in spherical coordinates in other scientific fields. We present an equivalent formulation of the spherical Fourier-Bessel decomposition that separates radial and tangential calculations. We propose the use of the existing pixelisation scheme HEALPix for a rapid calculation of the tangential modes. 3DEX (3D EXpansions) is a public code for fast spherical Fourier-Bessel decomposition of 3D all-sky surveys that takes advantage of HEALPix for the calculation of tangential modes. We perform tests on very large simulations and we compare the precision and computation time of our method with an optimised implementation of the spherical Fourier-Bessel original formulation. For surveys with millions of galaxies, computation time is reduced by a factor 4-12 depending on the desired scales and accuracy. The formulation is also suitable for pre-calculations and external storage of the spherical harmonics, which allows for additional speed improvements. The 3DEX code can accommodate data with masked regions of missing data. 3DEX can also be used in other disciplines, where 3D data are to be analysed in spherical coordinates. The code and documentation can be downloaded at http://ixkael.com/blog/3dex.

astro-ph.CO↗

arXiv2012

Wavelet Helmholtz decomposition for weak lensing mass map reconstruction

To derive the convergence field from the gravitational shear (gamma) of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanks to the Fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore, FFT implicitly uses periodic conditions that introduce errors to the reconstruction. A method has been proposed that relies on computation of an intermediate field u that combines the derivatives of gamma and on convolution with a Green kernel. In this paper, we study the wavelet Helmholtz decomposition as a new approach to reconstructing the dark matter mass map. We show that a link exists between the Helmholtz decomposition and the E/B mode separation. We introduce a new wavelet construction, that has a property that gives us more flexibility in handling the border problem, and we propose a new method of reconstructing the dark matter mass map in the wavelet space. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz decomposition reconstructs the borders better than all other existing methods.

astro-ph.CO↗

arXiv2012

Spherical 3D Isotropic Wavelets

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. 2006. We also present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel Discrete Spherical Fourier-Bessel Transform. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html

astro-ph.CO↗

arXiv2011

Detecting Baryon Acoustic Oscillations

Baryon Acoustic Oscillations are a feature imprinted in the galaxy distribution by acoustic waves traveling in the plasma of the early universe. Their detection at the expected scale in large-scale structures strongly supports current cosmological models with a nearly linear evolution from redshift approximately 1000, and the existence of dark energy. Besides, BAOs provide a standard ruler for studying cosmic expansion. In this paper we focus on methods for BAO detection using the correlation function measurement. For each method, we want to understand the tested hypothesis (the hypothesis H0 to be rejected) and the underlying assumptions. We first present wavelet methods which are mildly model-dependent and mostly sensitive to the BAO feature. Then we turn to fully model-dependent methods. We present the most often used method based on the chi^2 statistic, but we find it has limitations. In general the assumptions of the chi^2 method are not verified, and it only gives a rough estimate of the significance. The estimate can become very wrong when considering more realistic hypotheses, where the covariance matrix of the measurement depends on cosmological parameters. Instead we propose to use a new method based on two modifications: we modify the procedure for computing the significance and make it rigorous, and we modify the statistic to obtain better results in the case of varying covariance matrix. We verify with simulations that correct significances are different from the ones obtained using the classical chi^2 procedure. We also test a simple example of varying covariance matrix. In this case we find that our modified statistic outperforms the classical chi^2 statistic when both significances are correctly computed. Finally we find that taking into account variations of the covariance matrix can change both BAO detection levels and cosmological parameter constraints.

astro-ph.CO↗

arXiv2011

CMB map restoration

Estimating the cosmological microwave background is of utmost importance for cosmology. However, its estimation from full-sky surveys such as WMAP or more recently Planck is challenging: CMB maps are generally estimated via the application of some source separation techniques which never prevent the final map from being contaminated with noise and foreground residuals. These spurious contaminations whether noise or foreground residuals are well-known to be a plague for most cosmologically relevant tests or evaluations; this includes CMB lensing reconstruction or non-Gaussian signatures search. Noise reduction is generally performed by applying a simple Wiener filter in spherical harmonics; however this does not account for the non-stationarity of the noise. Foreground contamination is usually tackled by masking the most intense residuals detected in the map, which makes CMB evaluation harder to perform. In this paper, we introduce a novel noise reduction framework coined LIW-Filtering for Linear Iterative Wavelet Filtering which is able to account for the noise spatial variability thanks to a wavelet-based modeling while keeping the highly desired linearity of the Wiener filter. We further show that the same filtering technique can effectively perform foreground contamination reduction thus providing a globally cleaner CMB map. Numerical results on simulated but realistic Planck data are provided.

astro-ph.CO↗

arXiv2011

Measuring the Integrated Sachs-Wolfe Effect

One of the main challenges of modern cosmology is to understand the nature of dark energy. The Integrated Sachs-Wolfe (ISW) effect is sensitive to dark energy and presents an independent signature of dark energy in the absence of modified gravity and curvature. The ISW effect occurs on large scales, where cosmic variance is high and where there are large amounts of missing data in the CMB and large scale structure maps due to Galactic confusion. Moreover, existing methods in the literature often make strong assumptions about the statistics of the underlying fields or estimators. Together these effects can severely limit signal extraction. We review literature on the ISW effect, comparing statistical subtleties between existing methods, and identifying several limitations. We propose a novel method to detect and measure the ISW signal. This method assumes only that the primordial CMB field is Gaussian. It is based on a sparse inpainting method to reconstruct missing data and uses a bootstrap technique to avoid assumptions about the statistics of the estimator. It is a complete method, using three complementary statistical methods. We apply our method to Euclid-like simulations and show we can expect a \sim 7σmodel-independent detection of the ISW signal with WMAP7-like data, even with missing data. Other tests return \sim 4.7σdetection levels for a Euclid-like survey, with levels independent from whether the galaxy field is normally or lognormally distributed. We apply our method to the 2 Micron All Sky Survey (2MASS) and WMAP7 CMB data and find detections in the 1.1 - 2.0σrange, as expected from simulations. As a by-product, we reconstruct the full-sky temperature ISW field due to 2MASS data. We have presented a novel technique, based on sparse inpainting and bootstrapping, which accurately detects and reconstructs the ISW effect.

astro-ph.CO↗

arXiv2009

Reconstruction of the CMB lensing for Planck

We prepare real-life Cosmic Microwave Background (CMB) lensing extraction with the forthcoming Planck satellite data, by studying two systematic effects related to the foregrounds contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and of removing a large contaminated region of the sky. We first use the Generalized Morphological Component Analysis (GMCA) method to perform a component separation within a simplified framework which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then, restore them using a recent inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. We find that the foreground residuals from the GMCA method does not alter significantly the lensed signal, nor does the mask corrected with the inpainting method, even in the presence of point sources residuals.

astro-ph.CO↗

arXiv2009

Light on Dark Matter with Weak Gravitational Lensing

This paper reviews statistical methods recently developed to reconstruct and analyze dark matter mass maps from weak lensing observations. The field of weak lensing is motivated by the observations made in the last decades showing that the visible matter represents only about 4-5% of the Universe, the rest being dark. The Universe is now thought to be mostly composed by an invisible, pressureless matter -potentially relic from higher energy theories- called "dark matter" (20-21%) and by an even more mysterious term, described in Einstein equations as a vacuum energy density, called "dark energy" (70%). This "dark" Universe is not well described or even understood, so this point could be the next breakthrough in cosmology. Weak gravitational lensing is believed to be the most promising tool to understand the nature of dark matter and to constrain the cosmological model used to describe the Universe. Gravitational lensing is the process in which light from distant galaxies is bent by the gravity of intervening mass in the Universe as it travels towards us. This bending causes the image of background galaxies to appear slightly distorted and can be used to extract significant results for cosmology. Future weak lensing surveys are already planned in order to cover a large fraction of the sky with large accuracy. However this increased accuracy also places greater demands on the methods used to extract the available information. In this paper, we will first describe the important steps of the weak lensing processing to reconstruct the dark matter distribution from shear estimation. Then we will discuss the problem of statistical estimation in order to set constraints on the cosmological model. We review the methods which are currently used especially new methods based on sparsity.

astro-ph.CO↗

arXiv2009

Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope

The multiscale variance stabilization Transform (MSVST) has recently been proposed for Poisson data denoising. This procedure, which is nonparametric, is based on thresholding wavelet coefficients. We present in this paper an extension of the MSVST to 3D data (in fact 2D-1D data) when the third dimension is not a spatial dimension, but the wavelength, the energy, or the time. We show that the MSVST can be used for detecting and characterizing astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT was launched in June 2008 on the Fermi Gamma-ray Space Telescope mission. The MSVST algorithm is very fast relative to traditional likelihood model fitting, and permits efficient detection across the time dimension and immediate estimation of spectral properties. Astrophysical sources of gamma rays, especially active galaxies, are typically quite variable, and our current work may lead to a reliable method to quickly characterize the flaring properties of newly-detected sources.

astro-ph.IM↗

arXiv2009

Cosmological models discrimination with Weak Lensing

Weak gravitational lensing provides a unique method to map directly the dark matter in the Universe. The majority of lensing analyses uses the two-point statistics of the cosmic shear field to constrain the cosmological model yielding degeneracies, such as that between sigma_8 and Omega_M respectively the r.m.s. of the mass fluctuations at a scale of 8 Mpc/h and the matter density parameter both at z = 0. However, the two-point statistics only measure the Gaussian properties of the field and the weak lensing field is non-Gaussian. It has been shown that the estimation of non-Gaussian statistics on weak lensing data can improve the constraints on cosmological parameters. In this paper, we systematically compare a wide range of non-Gaussian estimators in order to determine which one provides tighter constraints on the cosmological parameters. These statistical methods include skewness, kurtosis and the Higher Criticism test in several sparse representations such as wavelet and curvelet; as well as the bispectrum, peak counting and a new introduced statistic called Wavelet Peak Counting (WPC). Comparisons based on sparse representations show that the wavelet transform is the most sensitive to non-Gaussian cosmological structures. It appears also that the best statistic for non-Gaussian characterization in weak lensing mass maps is the WPC. Finally, we show that the sigma_8 -Omega_m degeneracy could be even better broken if the WPC estimation is performed on weak lensing mass maps filtered by the wavelet method, MRLens.

astro-ph.CO↗