297,324 research outputs found
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.Comment: submitted to A&
How well do third-order aperture mass statistics separate E- and B-modes?
With 3rd-order statistics of gravitational shear it will be possible to
extract valuable cosmological information from ongoing and future weak lensing
surveys which is not contained in standard 2nd-order statistics, due to the
non-Gaussianity of the shear field. Aperture mass statistics are an appropriate
choice for 3rd-order statistics due to their simple form and their ability to
separate E- and B-modes of the shear. However, it has been demonstrated that
2nd-order aperture mass statistics suffer from E-/B-mode mixing because it is
impossible to reliably estimate the shapes of close pairs of galaxies. This
finding has triggered developments of several new 2nd-order statistical
measures for cosmic shear. Whether the same developments are needed for
3rd-order shear statistics is largely determined by how severe this E-/B-mixing
is for 3rd-order statistics. We test 3rd-order aperture mass statistics against
E-/B-mode mixing, and find that the level of contamination is well-described by
a function of , with being the
cut-off scale. At angular scales of , the
decrease in the E-mode signal due to E-/B-mode mixing is smaller than 1
percent, and the leakage into B-modes is even less. For typical small-scale
cut-offs this E-/B-mixing is negligible on scales larger than a few arcminutes.
Therefore, 3rd-order aperture mass statistics can safely be used to separate E-
and B-modes and infer cosmological information, for ground-based surveys as
well as forthcoming space-based surveys such as Euclid.Comment: references added, A&A publishe
An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation
We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a reliability of more than \%. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources
- …