42,774 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&
A fast approach for overcomplete sparse decomposition based on smoothed L0 norm
In this paper, a fast algorithm for overcomplete sparse decomposition, called
SL0, is proposed. The algorithm is essentially a method for obtaining sparse
solutions of underdetermined systems of linear equations, and its applications
include underdetermined Sparse Component Analysis (SCA), atomic decomposition
on overcomplete dictionaries, compressed sensing, and decoding real field
codes. Contrary to previous methods, which usually solve this problem by
minimizing the L1 norm using Linear Programming (LP) techniques, our algorithm
tries to directly minimize the L0 norm. It is experimentally shown that the
proposed algorithm is about two to three orders of magnitude faster than the
state-of-the-art interior-point LP solvers, while providing the same (or
better) accuracy.Comment: Accepted in IEEE Transactions on Signal Processing. For MATLAB codes,
see (http://ee.sharif.ir/~SLzero). File replaced, because Fig. 5 was missing
erroneousl
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