5,941 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
Nearly degenerate heavy sterile neutrinos in cascade decay: mixing and oscillations
Some extensions beyond the Standard Model propose the existence of nearly
degenerate heavy sterile neutrinos. If kinematically allowed these can be
resonantly produced and decay in a cascade to common final states. The common
decay channels lead to mixing of the heavy sterile neutrino states and
interference effects. We implement non-perturbative methods to study the
dynamics of the cascade decay to common final states, which features
similarities but also noteworthy differences with the case of neutral meson
mixing. We show that mixing and oscillations among the nearly degenerate
sterile neutrinos can be detected as \emph{quantum beats} in the distribution
of final states produced from their decay. These oscillations would be a
telltale signal of mixing between heavy sterile neutrinos. We study in detail
the case of two nearly degenerate sterile neutrinos produced in the decay of
pseudoscalar mesons and decaying into a purely leptonic "visible" channel:
. Possible cosmological implications for the
effective number of neutrinos are discussed.Comment: updated references, more comments, same results, published version.
arXiv admin note: text overlap with arXiv:1406.573
Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
Wavelets have been used extensively for several years now in astronomy for
many purposes, ranging from data filtering and deconvolution, to star and
galaxy detection or cosmic ray removal. More recent sparse representations such
ridgelets or curvelets have also been proposed for the detection of anisotropic
features such cosmic strings in the cosmic microwave background.
We review in this paper a range of methods based on sparsity that have been
proposed for astronomical data analysis. We also discuss what is the impact of
Compressed Sensing, the new sampling theory, in astronomy for collecting the
data, transferring them to the earth or reconstructing an image from incomplete
measurements.Comment: Submitted. Full paper will figures available at
http://jstarck.free.fr/IEEE09_SparseAstro.pd
On Preferred Axes in WMAP Cosmic Microwave Background Data after Subtraction of the Integrated Sachs-Wolfe Effect
There is currently a debate over the existence of claimed statistical
anomalies in the cosmic microwave background (CMB), recently confirmed in
Planck data. Recent work has focussed on methods for measuring statistical
significance, on masks and on secondary anisotropies as potential causes of the
anomalies. We investigate simultaneously the method for accounting for masked
regions and the foreground integrated Sachs-Wolfe (ISW) signal. We search for
trends in different years of WMAP CMB data with different mask treatments. We
reconstruct the ISW field due to the 2 Micron All-Sky Survey (2MASS) and the
NRAO VLA Sky Survey (NVSS) up to l=5, and we focus on the Axis of Evil (AoE)
statistic and even/odd mirror parity, both of which search for preferred axes
in the Universe. We find that removing the ISW reduces the significance of
these anomalies in WMAP data, though this does not exclude the possibility of
exotic physics. In the spirit of reproducible research, all reconstructed maps
and codes will be made available for download at
http://www.cosmostat.org/anomaliesCMB.html.Comment: Figure 1-2 and Tables 1, D.1, D.2 updated. Main conclusions
unchanged. Accepted for publication in A&A. In the spirit of reproducible
research, all statistical and sparse inpainting codes as well as resulting
products which constitute main results of this paper will be made public
here: http://www.cosmostat.org/anomaliesCMB.htm
3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis
Upcoming spectroscopic galaxy surveys are extremely promising to help in
addressing the major challenges of cosmology, in particular in understanding
the nature of the dark universe. The strength of these surveys comes from their
unprecedented depth and width. Optimal extraction of their three-dimensional
information is of utmost importance to best constrain the properties of the
dark universe. Although there is theoretical motivation and novel tools to
explore these surveys using the 3D spherical Fourier-Bessel (SFB) power
spectrum of galaxy number counts , most survey
optimisations and forecasts are based on the tomographic spherical harmonics
power spectrum . We performed a new investigation of the
information that can be extracted from the tomographic and 3D SFB techniques by
comparing the forecast cosmological parameter constraints obtained from a
Fisher analysis in the context of planned stage IV wide-field galaxy surveys.
The comparison was made possible by careful and coherent treatment of
non-linear scales in the two analyses. Nuisance parameters related to a scale-
and redshift-dependent galaxy bias were also included for the first time in the
computation of both the 3D SFB and tomographic power spectra. Tomographic and
3D SFB methods can recover similar constraints in the absence of systematics.
However, constraints from the 3D SFB analysis are less sensitive to unavoidable
systematics stemming from a redshift- and scale-dependent galaxy bias. Even for
surveys that are optimised with tomography in mind, a 3D SFB analysis is more
powerful. In addition, for survey optimisation, the figure of merit for the 3D
SFB method increases more rapidly with redshift, especially at higher
redshifts, suggesting that the 3D SFB method should be preferred for designing
and analysing future wide-field spectroscopic surveys.Comment: 12 pages, 6 Figures. Python package for cosmological forecasts
available at https://cosmicpy.github.io . Updated figures. Matches published
versio
Polarized wavelets and curvelets on the sphere
The statistics of the temperature anisotropies in the primordial cosmic
microwave background radiation field provide a wealth of information for
cosmology and for estimating cosmological parameters. An even more acute
inference should stem from the study of maps of the polarization state of the
CMB radiation. Measuring the extremely weak CMB polarization signal requires
very sensitive instruments. The full-sky maps of both temperature and
polarization anisotropies of the CMB to be delivered by the upcoming Planck
Surveyor satellite experiment are hence being awaited with excitement.
Multiscale methods, such as isotropic wavelets, steerable wavelets, or
curvelets, have been proposed in the past to analyze the CMB temperature map.
In this paper, we contribute to enlarging the set of available transforms for
polarized data on the sphere. We describe a set of new multiscale
decompositions for polarized data on the sphere, including decimated and
undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The
proposed transforms are invertible and so allow for applications in data
restoration and denoising.Comment: Accepted. Full paper will figures available at
http://jstarck.free.fr/aa08_pola.pd
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