203 research outputs found
Wavelets Applied to CMB Maps: a Multiresolution Analysis for Denoising
Analysis and denoising of Cosmic Microwave Background (CMB) maps are
performed using wavelet multiresolution techniques. The method is tested on
maps with resolution resembling the
experimental one expected for future high resolution space observations.
Semianalytic formulae of the variance of wavelet coefficients are given for the
Haar and Mexican Hat wavelet bases. Results are presented for the standard Cold
Dark Matter (CDM) model. Denoising of simulated maps is carried out by removal
of wavelet coefficients dominated by instrumental noise. CMB maps with a
signal-to-noise, , are denoised with an error improvement factor
between 3 and 5. Moreover we have also tested how well the CMB temperature
power spectrum is recovered after denoising. We are able to reconstruct the
's up to with errors always below in cases with
.Comment: latex file 9 pages + 5 postscript figures + 1 gif figure (figure 6),
to be published in MNRA
Contributions of point extragalactic sources to the Cosmic Microwave Background bispectrum
All the analyses of Cosmic Microwave Background (CMB) temperature maps
up--to--date show that CMB anisotropies follow a Gaussian distribution. On the
other hand, astrophysical foregrounds which hamper the detection of the CMB
angular power spectrum, are not Gaussian distributed on the sky. Therefore,
they should give a sizeable contribution to the CMB bispectrum. In fact, the
first year data of the Wilkinson Microwave Anisotropy Probe (WMAP) mission have
allowed the {\it first} detection of the extragalactic source contribution to
the CMB bispectrum at 41 GHz and, at the same time, much tighter limits than
before to non--Gaussian primordial fluctuations. In view of the above and for
achieving higher precision in current and future CMB measurements of
non--Gaussianity, in this paper we discuss a comprehensive assessment of the
bispectrum due to either uncorrelated and clustered extragalactic point sources
in the whole frequency interval around the CMB intensity peak. Our
calculations, based on current cosmological evolution models for sources, show
that the reduced angular bispectrum due to point sources, , should be
detectable in all WMAP and Planck frequency channels. We also find agreement
with the results on at 41 GHz coming from the analysis of the first
year WMAP data. Moreover, by comparing with the primordial reduced CMB
bispectrum, we find that only the peak value of the primordial bispectrum
(which appears at ) results greater than in a frequency
window around the intensity peak of the CMB. The amplitude of this window
basically depends on the capability of the source detection algorithms (i.e.,
on the achievable flux detection limit, , for sources).Comment: 26 pages, 6 Figures, use AasTex5.0, ApJ, in press, Oct. 10, 2003
Issu
Filter Design for the Detection/Estimation of the Modulus of a Vector. Application to Polarization Data
We consider a set of M images, whose pixel intensities at a common point can
be treated as the components of a M-dimensional vector. We are interested in
the estimation of the modulus of such a vector associated to a compact source.
For instance, the detection/estimation of the polarized signal of compact
sources immersed in a noisy background is relevant in some fields like
Astrophysics. We develop two different techniques, one based on the Maximum
Likelihood Estimator (MLE) applied to the modulus distribution, the modulus
filter (ModF) and other based on prefiltering the components before fusion, the
filtered fusion (FF), to deal with this problem. We present both methods in the
general case of M images and apply them to the particular case of three images
(linear plus circular polarization). Numerical simulations have been performed
to test these filters considering polarized compact sources immersed in
stationary noise. The FF performs better than the ModF in terms of errors in
the estimated amplitude and position of the source, especially in the low
signal-to-noise case. We also compare both methods with the direct application
of a matched filter (MF) on the polarization data. This last technique is
clearly outperformed by the new methods.Comment: 18 pages, 3 figures, accepted for publication in Signal Processin
Isotropic Wavelets: a Powerful Tool to Extract Point Sources from CMB Maps
It is the aim of this paper to introduce the use of isotropic wavelets to
detect and determine the flux of point sources appearing in CMB maps. The most
suited wavelet to detect point sources filtered with a Gaussian beam is the
Mexican Hat. An analytical expression of the wavelet coefficient obtained in
the presence of a point source is provided and used in the detection and flux
estimation methods presented. For illustration the method is applied to two
simulations (assuming Planck Mission characteristics) dominated by CMB (100
GHz) and dust (857 GHz) as these will be the two signals dominating at low and
high frequency respectively in the Planck channels. We are able to detect
bright sources above 1.58 Jy at 857 GHz (82% of all sources) and above 0.36 Jy
at 100 GHz (100% of all) with errors in the flux estimation below 25%. The main
advantage of this method is that nothing has to be assumed about the underlying
field, i.e. about the nature and properties of the signal plus noise present in
the maps. This is not the case in the detection method presented by Tegmark and
Oliveira-Costa 1998. Both methods are compared producing similar results.Comment: 6 pages. Accepted for publication in MNRA
Analysis of CMB maps with 2D wavelets
We consider the 2D wavelet transform with two scales to study sky maps of
temperature anisotropies in the cosmic microwave background radiation (CMB). We
apply this technique to simulated maps of small sky patches of size 12.8 \times
12.8 square degrees and 1.5' \times 1.5' pixels. The relation to the standard
approach, based on the cl's is established through the introduction of the
scalogram. We consider temperature fluctuations derived from standard, open and
flat-Lambda CDM models. We analyze CMB anisotropies maps plus uncorrelated
Gaussian noise (uniform and non-uniform) at idfferent S/N levels. We explore in
detail the denoising of such maps and compare the results with other techniques
already proposed in the literature. Wavelet methods provide a good
reconstruction of the image and power spectrum. Moreover, they are faster than
previously proposed methods.Comment: latex file 7 pages + 5 postscript files + 1 gif file; accepted for
publication in A&A
Non-blind catalogue of extragalactic point sources from the Wilkinson Microwave Anisotropy Probe (WMAP) first 3--year survey data
We have used the MHW2 filter to obtain estimates of the flux densities at the
WMAP frequencies of a complete sample of 2491 sources, mostly brighter than 500
mJy at 5 GHz, distributed over the whole sky excluding a strip around the
Galactic equator (b < 5 degrees). After having detected 933 sources above the 3
sigma level in the MHW2 filtered maps - our New Extragalactic WMAP Point Source
(NEWPS_3sigma) Catalogue - we are left with 381 sources above 5 sigma in at
least one WMAP channel, 369 of which constitute our NEWPS_5sigma catalogue. It
is remarkable to note that 98 (i.e. 26%) sources detected above 5 sigma are
`new', they are not present in the WMAP catalogue. Source fluxes have been
corrected for the Eddington bias. Our flux density estimates before such
correction are generally in good agreement with the WMAP ones at 23 GHz. At
higher frequencies WMAP fluxes tend to be slightly higher than ours, probably
because WMAP estimates neglect the deviations of the point spread function from
a Gaussian shape. On the whole, above the estimated completeness limit of 1.1
Jy at 23 GHz we detected 43 sources missed by the blind method adopted by the
WMAP team. On the other hand, our low-frequency selection threshold left out 25
WMAP sources, only 12 of which, however, are 5 sigma detections and only 3 have
fluxes S at 23 GHz > 1.1 Jy. Thus, our approach proved to be competitive with,
and complementary to the WMAP one.Comment: 18 pages, 6 figures, 5 tables. Accepted for publication in ApJ
Goodness-of-Fit Tests to study the Gaussianity of the MAXIMA data
Goodness-of-Fit tests, including Smooth ones, are introduced and applied to
detect non-Gaussianity in Cosmic Microwave Background simulations. We study the
power of three different tests: the Shapiro-Francia test (1972), the
uncategorised smooth test developed by Rayner and Best(1990) and the Neyman's
Smooth Goodness-of-fit test for composite hypotheses (Thomas and Pierce 1979).
The Smooth Goodness-of-Fit tests are designed to be sensitive to the presence
of ``smooth'' deviations from a given distribution. We study the power of these
tests based on the discrimination between Gaussian and non-Gaussian
simulations. Non-Gaussian cases are simulated using the Edgeworth expansion and
assuming pixel-to-pixel independence. Results show these tests behave similarly
and are more powerful than tests directly based on cumulants of order 3, 4, 5
and 6. We have applied these tests to the released MAXIMA data. The applied
tests are built to be powerful against detecting deviations from univariate
Gaussianity. The Cholesky matrix corresponding to signal (based on an assumed
cosmological model) plus noise is used to decorrelate the observations previous
to the analysis. Results indicate that the MAXIMA data are compatible with
Gaussianity.Comment: MNRAS, in pres
Spherical Mexican Hat wavelet: an application to detect non-Gaussianity in the COBE-DMR maps
The spherical Mexican Hat wavelet is introduced in this paper, with the aim
of testing the Gaussianity of the Cosmic Microwave Background temperature
fluctuations. Using the information given by the wavelet coefficients at
several scales, we have performed several statistical tests on the COBE-DMR
maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale-scale
correlations (for two and three scales) and Kolmogorov-Smirnov tests indicate
that the COBE-DMR data are consistent with a Gaussian distribution. We have
extended the analysis to compare temperature values provided by COBE-DMR data
with distributions (obtained from Gaussian simulations) at each pixel and at
each scale. The number of pixels with temperature values outside the 95% and
the 99% is consistent with that obtained from Gaussian simulations, at all
scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum
temperatures in the map) are also consistent with those obtained from Gaussian
simulations.Comment: to be published in MNRA
Forecasts on the contamination induced by unresolved point sources in primordial non-Gaussianity beyond Planck
In this paper we present forecasts of the contamination on different shapes of the
primordial non-Gaussianity fnl parameter \u2013 detectable on future Cosmic Microwave
Background (CMB) high\u2013resolution anisotropy maps \u2013 produced by unresolved ex-
tragalactic point sources at frequencies of cosmological interest (45\u2013375 GHz). We
consider two scenarios: an ideal (noiseless) mission and a possible future space-borne
satellite, with instrumental characteristics similar to the ones proposed for the Cos-
mic Origins Explorer (COrE). The local, equilateral, orthogonal and flat shapes are
considered in both temperature (intensity) and polarized emission data. The angular
power spectrum and bispectrum of extragalactic point sources are estimated by state-
of-the-art models of source number counts. The impact of all the most relevant (far\u2013IR
and radio selected) source populations on these shapes at COrE frequencies is studied.
The results of this analysis show that unresolved extragalactic point sources should
not induce a very relevant non-Gaussian signal in the frequency range 100\u2013200GHz,
thus not preventing a correct estimate of the CMB primordial fnl parameter. Polariza-
tion information allows one to significantly reduce the error\u2013bars in the fnl parameter
and the bias induced by unresolved sources and, hence, to widen the range of frequen-
cies for fnl studies. On the contrary, at \u3bd 225GHz, important
non-Gaussian deviations in CMB anisotropy maps are expected due to unresolved
extragalactic sources
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