909 research outputs found
Efficient and Robust Signal Detection Algorithms for the Communication Applications
Signal detection and estimation has been prevalent in signal processing and communications for many years. The relevant studies deal with the processing of information-bearing signals for the purpose of information extraction. Nevertheless, new robust and efficient signal detection and estimation techniques are still in demand since there emerge more and more practical applications which rely on them. In this dissertation work, we proposed several novel signal detection schemes for wireless communications applications, such as source localization algorithm, spectrum sensing method, and normality test. The associated theories and practice in robustness, computational complexity, and overall system performance evaluation are also provided
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&
Modeling sparse connectivity between underlying brain sources for EEG/MEG
We propose a novel technique to assess functional brain connectivity in
EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA),
can overcome the problem of volume conduction by modeling neural data
innovatively with the following ingredients: (a) the EEG is assumed to be a
linear mixture of correlated sources following a multivariate autoregressive
(MVAR) model, (b) the demixing is estimated jointly with the source MVAR
parameters, (c) overfitting is avoided by using the Group Lasso penalty. This
approach allows to extract the appropriate level cross-talk between the
extracted sources and in this manner we obtain a sparse data-driven model of
functional connectivity. We demonstrate the usefulness of SCSA with simulated
data, and compare to a number of existing algorithms with excellent results.Comment: 9 pages, 6 figure
On the linear term correction for needlets/wavelets non-Gaussianity estimators
We derive the linear correction term for needlet and wavelet estimators of
the bispectrum and the non-linearity parameter fNL on cosmic microwave
background radiation data. We show that on masked WMAP-like data with
anisotropic noise, the error bars improve by 10-20% and almost reach the
optimal error bars obtained with the KSW estimator (Komatsu et al 2005). In the
limit of full-sky and isotropic noise, this term vanishes. We apply needlet and
wavelet estimators to the WMAP 7-year data and obtain our best estimate
fNL=37.5 \pm 21.8.Comment: 10 pages, submitted to Ap
Statistical challenges in the analysis of Cosmic Microwave Background radiation
An enormous amount of observations on Cosmic Microwave Background radiation
has been collected in the last decade, and much more data are expected in the
near future from planned or operating satellite missions. These datasets are a
goldmine of information for Cosmology and Theoretical Physics; their efficient
exploitation posits several intriguing challenges from the statistical point of
view. In this paper we review a number of open problems in CMB data analysis
and we present applications to observations from the WMAP mission.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS190 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
General CMB bispectrum analysis using wavelets and separable modes
In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. This will be particularly important for upcoming surveys such as \emph{Planck}. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding \fnllocal=38.4 \pm 23.6 and \fnlequil=-119.2 \pm 123.6
The Cosmic Microwave Background & Inflation, Then & Now
Boomerang, Maxima, DASI, CBI and VSA significantly increase the case for
accelerated expansion in the early universe (the inflationary paradigm) and at
the current epoch (dark energy dominance), especially when combined with data
on high redshift supernovae (SN1) and large scale structure (LSS). There are
``7 pillars of Inflation'' that can be shown with the CMB probe, and at least
5, and possibly 6, of these have already been demonstrated in the CMB data: (1)
a large scale gravitational potential; (2) acoustic peaks/dips; (3) damping due
to shear viscosity; (4) a Gaussian (maximally random) distribution; (5)
secondary anisotropies; (6) polarization. A 7th pillar, anisotropies induced by
gravity wave quantum noise, could be too small. A minimal inflation parameter
set, \omega_b,\omega_{cdm}, \Omega_{tot}, \Omega_Q,w_Q,n_s,\tau_C, \sigma_8},
is used to illustrate the power of the current data. We find the CMB+LSS+SN1
data give \Omega_{tot} =1.00^{+.07}_{-.03}, consistent with (non-baroque)
inflation theory. Restricting to \Omega_{tot}=1, we find a nearly scale
invariant spectrum, n_s =0.97^{+.08}_{-.05}. The CDM density, \Omega_{cdm}{\rm
h}^2 =.12^{+.01}_{-.01}, and baryon density, \Omega_b {\rm h}^2 =
>.022^{+.003}_{-.002}, are in the expected range. (The Big Bang nucleosynthesis
estimate is 0.019\pm 0.002.) Substantial dark (unclustered) energy is inferred,
\Omega_Q \approx 0.68 \pm 0.05, and CMB+LSS \Omega_Q values are compatible with
the independent SN1 estimates. The dark energy equation of state, crudely
parameterized by a quintessence-field pressure-to-density ratio w_Q, is not
well determined by CMB+LSS (w_Q < -0.4 at 95% CL), but when combined with SN1
the resulting w_Q < -0.7 limit is quite consistent with the w_Q=-1 cosmological
constant case.Comment: 20 pages, 8 figures, in Theoretical Physics, MRST 2002: A Tribute to
George Libbrandt (AIP), eds. V. Elias, R. Epp, R. Myer
Real space tests of the statistical isotropy and Gaussianity of the WMAP CMB data
ABRIDGED: We introduce and analyze a method for testing statistical isotropy
and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature
maps, and cross-channel difference maps. We divide the sky into regions of
varying size and shape and measure the first four moments of the one-point
distribution within these regions, and using their simulated spatial
distributions we test the statistical isotropy and Gaussianity hypotheses. By
randomly varying orientations of these regions, we sample the underlying CMB
field in a new manner, that offers a richer exploration of the data content,
and avoids possible biasing due to a single choice of sky division. The
statistical significance is assessed via comparison with realistic Monte-Carlo
simulations.
We find the three-year WMAP maps to agree well with the isotropic, Gaussian
random field simulations as probed by regions corresponding to the angular
scales ranging from 6 deg to 30 deg at 68% confidence level. We report a
strong, anomalous (99.8% CL) dipole ``excess'' in the V band of the three-year
WMAP data and also in the V band of the WMAP five-year data (99.3% CL). We
notice the large scale hemispherical power asymmetry, and find that it is not
highly statistically significant in the WMAP three-year data (<~ 97%) at scales
l <= 40. The significance is even smaller if multipoles up to l=1024 are
considered (~90% CL). We give constraints on the amplitude of the
previously-proposed CMB dipole modulation field parameter. We easily detect the
residual foregrounds in cross-band difference maps at rms level <~ 7 \mu K (at
scales >~ 6 deg) and limit the systematical uncertainties to <~ 1.7 \mu K (at
scales >~ 30 deg).Comment: 20 pages, 20 figures; more tests added; updated to match the version
to be published in JCA
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