1,691 research outputs found
Wavelets, ridgelets and curvelets on the sphere
We present in this paper new multiscale transforms on the sphere, namely the
isotropic undecimated wavelet transform, the pyramidal wavelet transform, the
ridgelet transform and the curvelet transform. All of these transforms can be
inverted i.e. we can exactly reconstruct the original data from its
coefficients in either representation. Several applications are described. We
show how these transforms can be used in denoising and especially in a Combined
Filtering Method, which uses both the wavelet and the curvelet transforms, thus
benefiting from the advantages of both transforms. An application to component
separation from multichannel data mapped to the sphere is also described in
which we take advantage of moving to a wavelet representation.Comment: Accepted for publication in A&A. Manuscript with all figures can be
downloaded at http://jstarck.free.fr/aa_sphere05.pd
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
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
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
Statistical properties of dust far-infrared emission
The description of the statistical properties of dust emission gives
important constraints on the physics of the interstellar medium but it is also
a useful way to estimate the contamination of diffuse interstellar emission in
the cases where it is considered a nuisance. The main goals of this analysis of
the power spectrum and non-Gaussian properties of 100 micron dust emission are
1) to estimate the power spectrum of interstellar matter density in three
dimensions, 2) to review and extend previous estimates of the cirrus noise due
to dust emission and 3) to produce simulated dust emission maps that reproduce
the observed statistical properties. The main results are the following. 1) The
cirrus noise level as a function of brightness has been previously
overestimated. It is found to be proportional to instead of ^1.5, where
is the local average brightness at 100 micron. This scaling is in
accordance with the fact that the brightness fluctuation level observed at a
given angular scale on the sky is the sum of fluctuations of increasing
amplitude with distance on the line of sight. 2) The spectral index of dust
emission at scales between 5 arcmin and 12.5 degrees is =-2.9 on average
but shows significant variations over the sky. Bright regions have
systematically steeper power spectra than diffuse regions. 3) The skewness and
kurtosis of brightness fluctuations is high, indicative of strong
non-Gaussianity. 4) Based on our characterization of the 100 micron power
spectrum we provide a prescription of the cirrus confusion noise as a function
of wavelength and scale. 5) Finally we present a method based on a modification
of Gaussian random fields to produce simulations of dust maps which reproduce
the power spectrum and non-Gaussian properties of interstellar dust emission.Comment: 13 pages, 13 figures. Accepted for publication in A&
Phylogeny and Evolutionary History of the Amniote Egg
We review morphological features of the amniote egg and embryos in a comparative phylogenetic framework, including all major clades of extant vertebrates. We discuss 40 characters that are relevant for an analysis of the evolutionary history of the vertebrate egg. Special attention is given to the morphology of the cellular yolk sac, the eggshell, and extraembryonic membranes. Many features that are typically assigned to amniotes, such as a large yolk sac, delayed egg deposition, and terrestrial reproduction have evolved independently and convergently in numerous clades of vertebrates. We use phylogenetic character mapping and ancestral character state reconstruction as tools to recognize sequence, order, and patterns of morphological evolution and deduce a hypothesis of the evolutionary history of the amniote egg. Besides amnion and chorioallantois, amniotes ancestrally possess copulatory organs (secondarily reduced in most birds), internal fertilization, and delayed deposition of eggs that contain an embryo in the primitive streak or early somite stage. Except for the amnion, chorioallantois, and amniote type of eggshell, these features evolved convergently in almost all major clades of aquatic vertebrates possibly in response to selective factors such as egg predation, hostile environmental conditions for egg development, or to adjust hatching of young to favorable season. A functionally important feature of the amnion membrane is its myogenic contractility that moves the (early) embryo and prevents adhering of the growing embryo to extraembryonic materials. This function of the amnion membrane and the liquid-filled amnion cavity may have evolved under the requirements of delayed deposition of eggs that contain developing embryos. The chorioallantois is a temporary embryonic exchange organ that supports embryonic development. A possible evolutionary scenario is that the amniote egg presents an exaptation that paved the evolutionary pathway for reproduction on land. As shown by numerous examples from anamniotes, reproduction on land has occurred multiple times among vertebrates—the amniote egg presenting one “solution” that enabled the conquest of land for reproduction
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