1,162 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
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
Planck CMB Anomalies: Astrophysical and Cosmological Secondary Effects and the Curse of Masking
Large-scale anomalies have been reported in CMB data with both WMAP and
Planck data. These could be due to foreground residuals and or systematic
effects, though their confirmation with Planck data suggests they are not due
to a problem in the WMAP or Planck pipelines. If these anomalies are in fact
primordial, then understanding their origin is fundamental to either validate
the standard model of cosmology or to explore new physics. We investigate three
other possible issues: 1) the trade-off between minimising systematics due to
foreground contamination (with a conservative mask) and minimising systematics
due to masking, 2) astrophysical secondary effects (the kinetic Doppler
quadrupole and kinetic Sunyaev-Zel'dovich effect), and 3) secondary
cosmological signals (the integrated Sachs-Wolfe effect). We address the
masking issue by considering new procedures that use both WMAP and Planck to
produce higher quality full-sky maps using the sparsity methodology (LGMCA
maps). We show the impact of masking is dominant over that of residual
foregrounds, and the LGMCA full-sky maps can be used without further processing
to study anomalies. We consider four official Planck PR1 and two LGMCA CMB
maps. Analysis of the observed CMB maps shows that only the low quadrupole and
quadrupole-octopole alignment seem significant, but that the planar octopole,
Axis of Evil, mirror parity and cold spot are not significant in nearly all
maps considered. After subtraction of astrophysical and cosmological secondary
effects, only the low quadrupole may still be considered anomalous, meaning the
significance of only one anomaly is affected by secondary effect subtraction
out of six anomalies considered. In the spirit of reproducible research all
reconstructed maps and codes will be made available for download here
http://www.cosmostat.org/anomaliesCMB.html.Comment: Summary of results given in Table 2. Accepted for publication in
JCAP, 4th August 201
PRISM: 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. Here, we introduce a new method to estimate
this spectrum from the empirical power spectrum of cosmic microwave background
(CMB) maps.
A sparsity-based linear inversion method, coined \textbf{PRISM}, is
presented. This technique leverages a sparsity prior on features in the
primordial power spectrum in a wavelet basis to regularise the inverse problem.
This non-parametric approach does not assume a strong prior on the shape of the
primordial power spectrum, yet is able to correctly reconstruct its global
shape as well as localised features. These advantages make this method robust
for detecting deviations from the currently favoured scale-invariant spectrum.
We investigate the strength of this method on a set of WMAP 9-year simulated
data for three types of primordial power spectra: a nearly scale-invariant
spectrum, a spectrum with a small running of the spectral index, and a spectrum
with a localised feature. This technique proves to easily detect deviations
from a pure scale-invariant power spectrum and is suitable for distinguishing
between simple models of the inflation. We process the WMAP 9-year data and
find no significant departure from a nearly scale-invariant power spectrum with
the spectral index .
A high resolution primordial power spectrum can be reconstructed with this
technique, where any strong local deviations or small global deviations from a
pure scale-invariant spectrum can easily be detected
Joint Planck and WMAP CMB Map Reconstruction
We present a novel estimate of the cosmological microwave background (CMB)
map by combining the two latest full-sky microwave surveys: WMAP nine-year and
Planck PR1. The joint processing benefits from a recently introduced component
separation method coined "local-generalized morphological component analysis''
(LGMCA) based on the sparse distribution of the foregrounds in the wavelet
domain. The proposed estimation procedure takes advantage of the IRIS 100
micron as an extra observation on the galactic center for enhanced dust
removal. We show that this new CMB map presents several interesting aspects: i)
it is a full sky map without using any inpainting or interpolating method, ii)
foreground contamination is very low, iii) the Galactic center is very clean,
with especially low dust contamination as measured by the cross-correlation
between the estimated CMB map and the IRIS 100 micron map, and iv) it is free
of thermal SZ contamination.Comment: Astronomy and Astrophysics, accepte
Darth Fader: Using wavelets to obtain accurate redshifts of spectra at very low signal-to-noise
We present the DARTH FADER algorithm, a new wavelet-based method for
estimating redshifts of galaxy spectra in spectral surveys that is particularly
adept in the very low SNR regime. We use a standard cross-correlation method to
estimate the redshifts of galaxies, using a template set built using a PCA
analysis on a set of simulated, noise-free spectra. Darth Fader employs wavelet
filtering to both estimate the continuum & to extract prominent line features
in each galaxy spectrum. A simple selection criterion based on the number of
features present in the spectrum is then used to clean the catalogue: galaxies
with fewer than six total features are removed as we are unlikely to obtain a
reliable redshift estimate. Applying our wavelet-based cleaning algorithm to a
simulated testing set, we successfully build a clean catalogue including
extremely low signal-to-noise data (SNR=2.0), for which we are able to obtain a
5.1% catastrophic failure rate in the redshift estimates (compared with 34.5%
prior to cleaning). We also show that for a catalogue with uniformly mixed SNRs
between 1.0 & 20.0, with realistic pixel-dependent noise, it is possible to
obtain redshifts with a catastrophic failure rate of 3.3% after cleaning (as
compared to 22.7% before cleaning). Whilst we do not test this algorithm
exhaustively on real data, we present a proof of concept of the applicability
of this method to real data, showing that the wavelet filtering techniques
perform well when applied to some typical spectra from the SDSS archive. The
Darth Fader algorithm provides a robust method for extracting spectral features
from very noisy spectra. The resulting clean catalogue gives an extremely low
rate of catastrophic failures, even when the spectra have a very low SNR. For
very large sky surveys, this technique may offer a significant boost in the
number of faint galaxies with accurately determined redshifts.Comment: 22 pages, 15 figures. Accepted for publication in Astronomy &
Astrophysic
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