1,900 research outputs found
Low-l CMB Analysis and Inpainting
Reconstruction of the CMB in the Galactic plane is extremely difficult due to
the dominant foreground emissions such as Dust, Free-Free or Synchrotron. For
cosmological studies, the standard approach consists in masking this area where
the reconstruction is not good enough. This leads to difficulties for the
statistical analysis of the CMB map, especially at very large scales (to study
for e.g., the low quadrupole, ISW, axis of evil, etc). We investigate in this
paper how well some inpainting techniques can recover the low- spherical
harmonic coefficients. We introduce three new inpainting techniques based on
three different kinds of priors: sparsity, energy and isotropy, and we compare
them. We show that two of them, sparsity and energy priors, can lead to
extremely high quality reconstruction, within 1% of the cosmic variance for a
mask with Fsky larger than 80%.Comment: Submitte
Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
A crucial aspect of mass-mapping, via weak lensing, is quantification of the
uncertainty introduced during the reconstruction process. Properly accounting
for these errors has been largely ignored to date. We present results from a
new method that reconstructs maximum a posteriori (MAP) convergence maps by
formulating an unconstrained Bayesian inference problem with Laplace-type
-norm sparsity-promoting priors, which we solve via convex
optimization. Approaching mass-mapping in this manner allows us to exploit
recent developments in probability concentration theory to infer theoretically
conservative uncertainties for our MAP reconstructions, without relying on
assumptions of Gaussianity. For the first time these methods allow us to
perform hypothesis testing of structure, from which it is possible to
distinguish between physical objects and artifacts of the reconstruction. Here
we present this new formalism, demonstrate the method on illustrative examples,
before applying the developed formalism to two observational datasets of the
Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520
dataset can conclusively determine the physicality of individual local massive
substructure at significant confidence. However, in both cases the recovered
MAP estimators are consistent with both sets of data
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
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