235 research outputs found
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- 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%.Comment: Submitte
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
Sparsity and morphological diversity for hyperspectral data analysis
Recently morphological diversity and sparsity have
emerged as new and effective sources of diversity for
Blind Source Separation. Based on these new concepts,
novelmethods such as Generalized Morphological Component
Analysis have been put forward. The latter takes
advantage of the very sparse representation of structured
data in large overcomplete dictionaries, to separate
sources based on their morphology. Building on GMCA,
the purpose of this contribution is to describe a new algorithm
for hyperspectral data processing. Large-scale
hyperspectral data refers to collected data that exhibit
sparse spectral signatures in addition to sparse spatial
morphologies, in specified dictionaries of spectral and
spatial waveforms. Numerical experiments are reported
which demonstrate the validity of the proposed extension
for solving source separation problems involving
hyperspectral data
True CMB Power Spectrum Estimation
The cosmic microwave background (CMB) power spectrum is a powerful
cosmological probe as it entails almost all the statistical information of the
CMB perturbations. Having access to only one sky, the CMB power spectrum
measured by our experiments is only a realization of the true underlying
angular power spectrum. In this paper we aim to recover the true underlying CMB
power spectrum from the one realization that we have without a need to know the
cosmological parameters. The sparsity of the CMB power spectrum is first
investigated in two dictionaries; Discrete Cosine Transform (DCT) and Wavelet
Transform (WT). The CMB power spectrum can be recovered with only a few
percentage of the coefficients in both of these dictionaries and hence is very
compressible in these dictionaries. We study the performance of these
dictionaries in smoothing a set of simulated power spectra. Based on this, we
develop a technique that estimates the true underlying CMB power spectrum from
data, i.e. without a need to know the cosmological parameters. This smooth
estimated spectrum can be used to simulate CMB maps with similar properties to
the true CMB simulations with the correct cosmological parameters. This allows
us to make Monte Carlo simulations in a given project, without having to know
the cosmological parameters. The developed IDL code, TOUSI, for Theoretical
pOwer spectrUm using Sparse estImation, will be released with the next version
of ISAP
Sparsity constraints for hyperspectral data analysis: linear mixture model and beyond
The recent development of multi-channel sensors has motivated interest in devising new methods for the coherent processing of multivariate data. An extensive work has already been dedicated to multivariate data processing ranging from blind source separation (BSS) to multi/hyper-spectral data restoration. Previous work has emphasized on the fundamental role played by sparsity and morphological diversity to enhance multichannel signal processing. GMCA is a recent algorithm for multichannel data analysis which was used successfully in a variety of applications including multichannel sparse decomposition, blind source separation (BSS), color image restoration and inpainting. Inspired by GMCA, a recently introduced algorithm coined HypGMCA is described for BSS applications in hyperspectral data processing. It assumes the collected data is a linear instantaneous mixture of components exhibiting sparse spectral signatures as well as sparse spatial morphologies, each in specified dictionaries of spectral and spatial waveforms. We report on numerical experiments with synthetic data and application to real observations which demonstrate the validity of the proposed method
SZ and CMB reconstruction using Generalized Morphological Component Analysis
In the last decade, the study of cosmic microwave background (CMB) data has
become one of the most powerful tools to study and understand the Universe.
More precisely, measuring the CMB power spectrum leads to the estimation of
most cosmological parameters. Nevertheless, accessing such precious physical
information requires extracting several different astrophysical components from
the data. Recovering those astrophysical sources (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) thus amounts to a component separation problem which
has already led to an intense activity in the field of CMB studies. In this
paper, we introduce a new sparsity-based component separation method coined
Generalized Morphological Component Analysis (GMCA). The GMCA approach is
formulated in a Bayesian maximum a posteriori (MAP) framework. Numerical
results show that this new source recovery technique performs well compared to
state-of-the-art component separation methods already applied to CMB data.Comment: 11 pages - Statistical Methodology - Special Issue on Astrostatistics
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Blind Source Separation: the Sparsity Revolution
International audienceOver the last few years, the development of multi-channel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsity-based BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation
Application of a multidimensional wavelet denoising algorithm for the detection and characterization of astrophysical sources of gamma rays
International audienceZhang, Fadili, & Starck have recently developed a denoising procedure for Poisson data that offers advantages over other methods of intensity estimation in multiple dimensions. Their procedure, which is nonparametric, is based on thresholding wavelet coefficients. The restoration algorithm applied after thresholding provides good conservation of source flux. We present an investigation of the procedure of Zhang et al. for the detection and characterization of astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT is to be launched in late 2007 on the Gamma-ray Large Area Space Telescope mission. Source detection in the LAT data is complicated by the low fluxes of point sources relative to the diffuse celestial background, the limited angular resolution, and the tremendous variation of that resolution with energy (from tens of degrees at 30 MeV to 0.1â—¦ at 10 GeV). The algorithm is very fast relative to traditional likelihood model fitting, and permits 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
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.Comment: Accepted. Full paper will figures available at
http://jstarck.free.fr/aa08_msvst.pd
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