1,588 research outputs found
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
A fast and accurate first-order algorithm for compressed sensing
This paper introduces a new, fast and accurate algorithm
for solving problems in the area of compressed sensing,
and more generally, in the area of signal and image reconstruction
from indirect measurements. This algorithm
is inspired by recent progress in the development of novel
first-order methods in convex optimization, most notably
Nesterov’s smoothing technique. In particular, there is a
crucial property thatmakes thesemethods extremely efficient
for solving compressed sensing problems. Numerical
experiments show the promising performance of our
method to solve problems which involve the recovery of
signals spanning a large dynamic range
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
Sparse and Non-Negative BSS for Noisy Data
Non-negative blind source separation (BSS) has raised interest in various
fields of research, as testified by the wide literature on the topic of
non-negative matrix factorization (NMF). In this context, it is fundamental
that the sources to be estimated present some diversity in order to be
efficiently retrieved. Sparsity is known to enhance such contrast between the
sources while producing very robust approaches, especially to noise. In this
paper we introduce a new algorithm in order to tackle the blind separation of
non-negative sparse sources from noisy measurements. We first show that
sparsity and non-negativity constraints have to be carefully applied on the
sought-after solution. In fact, improperly constrained solutions are unlikely
to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA
(non-negative Generalized Morphological Component Analysis), makes use of
proximal calculus techniques to provide properly constrained solutions. The
performance of nGMCA compared to other state-of-the-art algorithms is
demonstrated by numerical experiments encompassing a wide variety of settings,
with negligible parameter tuning. In particular, nGMCA is shown to provide
robustness to noise and performs well on synthetic mixtures of real NMR
spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal
Processin
Battery
The usage of "battery" to describe a group electrical devices dates to Benjamin Franklin, who in 1748 described multiple Leyden jars by analogy to a battery of cannon (Benjamin Franklin borrowed the term "battery" from the military, which refers to weapons functioning together). Alessandro Volta described the first electrochemical battery, the voltaic pile in 1800. This was a stack of copper and zinc plates, separated by brine soaked paper disks, that could produce a steady current for a considerable length of time. Volta did not appreciate that the voltage was due to chemical reactions. He thought that his cells were an inexhaustible source of energy and that the associated corrosion effects at the electrodes were a mere nuisance, rather than an unavoidable consequence of their operation, as Michael Faraday showed in 1834.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3498
CMB map restoration
Estimating the cosmological microwave background is of utmost importance for
cosmology. However, its estimation from full-sky surveys such as WMAP or more
recently Planck is challenging: CMB maps are generally estimated via the
application of some source separation techniques which never prevent the final
map from being contaminated with noise and foreground residuals. These spurious
contaminations whether noise or foreground residuals are well-known to be a
plague for most cosmologically relevant tests or evaluations; this includes CMB
lensing reconstruction or non-Gaussian signatures search. Noise reduction is
generally performed by applying a simple Wiener filter in spherical harmonics;
however this does not account for the non-stationarity of the noise. Foreground
contamination is usually tackled by masking the most intense residuals detected
in the map, which makes CMB evaluation harder to perform. In this paper, we
introduce a novel noise reduction framework coined LIW-Filtering for Linear
Iterative Wavelet Filtering which is able to account for the noise spatial
variability thanks to a wavelet-based modeling while keeping the highly desired
linearity of the Wiener filter. We further show that the same filtering
technique can effectively perform foreground contamination reduction thus
providing a globally cleaner CMB map. Numerical results on simulated but
realistic Planck data are provided
Sparsity and adaptivity for the blind separation of partially correlated sources
Blind source separation (BSS) is a very popular technique to analyze
multichannel data. In this context, the data are modeled as the linear
combination of sources to be retrieved. For that purpose, standard BSS methods
all rely on some discrimination principle, whether it is statistical
independence or morphological diversity, to distinguish between the sources.
However, dealing with real-world data reveals that such assumptions are rarely
valid in practice: the signals of interest are more likely partially
correlated, which generally hampers the performances of standard BSS methods.
In this article, we introduce a novel sparsity-enforcing BSS method coined
Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve
sparse and partially correlated sources. More precisely, it makes profit of an
adaptive re-weighting scheme to favor/penalize samples based on their level of
correlation. Extensive numerical experiments have been carried out which show
that the proposed method is robust to the partial correlation of sources while
standard BSS techniques fail. The AMCA algorithm is evaluated in the field of
astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin
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