arXiv subjects

R. B. Barreiro

Publications and source records attributed to R. B. Barreiro.

288 records · Page 16Linked to original sources

arXiv2003

Goodness-of-fit tests of Gaussianity: constraints on the cumulants of the MAXIMA data

In this work, goodness-of-fit tests are adapted and applied to CMB maps to detect possible non-Gaussianity. We use Shapiro-Francia test and two Smooth goodness-of-fit tests: one developed by Rayner and Best and another one developed by Thomas and Pierce. The Smooth tests test small and smooth deviations of a prefixed probability function (in our case this is the univariate Gaussian). Also, the Rayner and Best test informs us of the kind of non-Gaussianity we have: excess of skewness, of kurtosis, and so on. These tests are optimal when the data are independent. We simulate and analyse non-Gaussian signals in order to study the power of these tests. These non-Gaussian simulations are constructed using the Edgeworth expansion, and assuming pixel-to-pixel independence. As an application, we test the Gaussianity of the MAXIMA data. Results indicate that the MAXIMA data are compatible with Gaussianity. Finally, the values of the skewness and kurtosis of MAXIMA data are constrained by |S| \le 0.035 and |K| \le 0.036 at the 99% confidence level.

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arXiv2003

Comparing filters for the detection of point sources

This paper considers filters (the Mexican hat wavelet, the matched and the scale-adaptive filters) that optimize the detection/separation of point sources on a background. We make a one-dimensional treatment, we assume that the sources have a Gaussian profile, i. e. $τ(x) = e^{- x^2/2R^2}$, and a background modelled by an homogeneous and isotropic Gaussian random field, characterised by a power spectrum $P(q)\propto q^{-γ}, γ\geq 0$. Local peak detection is used after filtering. Then, the Neyman-Pearson criterion is used to define the confidence level for detections and a comparison of filters is done based on the number of spurious and true detections. We have performed numerical simulations to test theoretical ideas and conclude that the results of the simulations agree with the analytical results.

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arXiv2002

Filtering techniques for the detection of Sunyaev-Zel'dovich clusters in multifrequency CMB maps

The problem of detecting Sunyaev-Zel'dovich (SZ) clusters in multifrequency CMB observations is investigated using a number of filtering techniques. A multifilter approach is introduced, which optimizes the detection of SZ clusters on microwave maps. An alternative method is also investigated, in which maps at different frequencies are combined in an optimal manner so that existing filtering techniques can be applied to the single combined map. The SZ profiles are approximated by the circularly-symmetric template $τ(x) = [1 +(x/r_c)^2]^{-λ}$, with $λ\simeq \tfrac{1}{2}$ and $x\equiv |\vec{x}|$, where the core radius $r_c$ and the overall amplitude of the effect are not fixed a priori, but are determined from the data. The background emission is modelled by a homogeneous and isotropic random field, characterized by a cross-power spectrum $P_{ν_1 ν_2}(q)$ with $q\equiv |\vec{q}|$. The filtering methods are illustrated by application to simulated Planck observations of a $12.8^\circ \times 12.8^\circ$ patch of sky in 10 frequency channels. Our simulations suggest that the Planck instrument should detect $\approx 10000$ SZ clusters in 2/3 of the sky. Moreover, we find the catalogue to be complete for fluxes $S > 170$ mJy at 300 GHz.

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arXiv2002

Scale-Adaptive filters for the detection/separation of compact sources

This paper presents scale-adaptive filters that optimize the detection/separation of compact sources on a background. We assume that the sources have a multiquadric profile, i. e. $τ(x) = {[1 + {(x/r_c)}^2]}^{-λ}, λ\geq {1/2}, x\equiv |\vec{x}|$, and a background modeled by a homogeneous and isotropic random field, characterized by a power spectrum $P(q)\propto q^{-γ}, γ\geq 0, q\equiv |\vec{q}|$. We make an n-dimensional treatment but consider two interesting astrophysical applications related to clusters of galaxies (Sunyaev-Zel'dovich effect and X-ray emission).

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arXiv2001

Combining maximum-entropy and the mexican hat wavelet to reconstruct the microwave sky

We present a maximum-entropy method (MEM) and `Mexican Hat' wavelet (MHW) joint analysis to recover the different components of the microwave sky from simulated observations by the ESA Planck satellite in a small patch of the sky. This combined method allows one to improve the CMB, Sunyaev-Zel'dovich and Galactic foregrounds separation achieved by the MEM technique alone. In particular, the reconstructed CMB map is free from any bright point source contamination. The joint analysis also produces point source catalogues at each Planck frequency which are more complete and accurate than those obtained by each method on its own. The results are especially improved at high frequencies where infrared galaxies dominate the point source contribution. Although this joint technique has been performed on simulated Planck data, it could be easily applied to other multifrequency CMB experiments, such as the forthcoming NASA MAP satellite or the recently performed Boomerang and MAXIMA experiments.

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arXiv2001

Regularization and Inverse Problems

An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon method, using examples from both astronomical and non-astronomical applications.

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arXiv2001

The discriminating power of wavelets to detect non-Gaussianity in the CMB

We investigate the power of wavelet techniques in detecting non-Gaussianity in the cosmic microwave background (CMB). We use the method to discriminate between an inflationary and a cosmic strings model using small simulated patches of the sky. We show the importance of the choice of a good test statistic in order to optimise the discriminating power of the wavelet technique. In particular, we construct the Fisher discriminant function, which combines all the information available in the different wavelet scales. We also compare the performance of different decomposition schemes and wavelet bases. For our case, we find that the Mallat and {\it à trous} algorithms are superior to the 2D-tensor wavelets. Using this technique, the inflationary and strings models are clearly distinguished even in the presence of a superposed Gaussian component with twice the rms amplitude of the original cosmic string map.

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arXiv2000

Combined MEM and MHW analysis of CMB observations

We present a combined maximum-entropy method (MEM) and Mexican Hat wavelet (MHW) analysis in order to recover the different components of the microwave sky. We apply this technique to simulated observations by the ESA Planck satellite in small patches of the sky. In particular, the introduction of the MHW allows one to detect and subtract the brightest point sources present in the input data and therefore to improve the reconstructions of the CMB and foreground components achieved by MEM on its own. In addition, a point source catalogue at each Planck frequency is produced, which is more complete and accurate than those obtained by each technique independently.

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arXiv2000

Geometrical estimators as a test of Gaussianity in the CMB

We investigate the power of geometrical estimators on detecting non-Gaussianity in the cosmic microwave background. In particular the number, eccentricity and Gaussian curvature of excursion sets above (and below) a threshold are studied. We compare their different performance when applied to non-Gaussian simulated maps of small patches of the sky, which take into account the angular resolution and instrumental noise of the Planck satellite. These non-Gaussian simulations are obtained as perturbations of a Gaussian field in two different ways which introduce a small level of skewness or kurtosis in the distribution. A comparison with a classical estimator, the genus, is also shown. We find that the Gaussian curvature is the best of our estimators in all the considered cases. Therefore we propose the use of this quantity as a particularly useful test to look for non-Gaussianity in the CMB.

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arXiv2000

Looking for non-Gaussianity in the COBE-DMR data with spherical wavelets

We present an analysis of the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) based on spherical wavelets. The skewness, kurtosis and scale-scale correlation spectra are computed from the detail wavelet coefficients at each scale. The sensitivity of the method to the orientation of the data is also taken into account. We find a single detection of non-Gaussianity at the $>99%$ confidence level in one of our statistics. We use Monte-Carlo simulations to assess the statistical significance of this detection and find that the probability of obtaining such a detection by chance for an underlying Gaussian field is as high as 0.69. Therefore, our analysis does not show evidence of non-Gaussianity in the COBE-DMR data.

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arXiv2000

Testing the Gaussianity of the COBE-DMR data with spherical wavelets

We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale-scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at $> 99$ per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaining such a detection by chance for an underlying Gaussian field is 0.69. Therefore, we conclude that the spherical wavelet technique shows no strong evidence of non-Gaussianity in the COBE-DMR data.

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arXiv1999

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.

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arXiv1999

The Cosmic Microwave Background: State of the Art

We review the current status of the cosmic microwave background (CMB) radiation, including a brief discussion of some basic theoretical aspects as well as a summary of anisotropy detections and CMB experiments. We focus on the description of some relevant characteristics of the microwave foregrounds, on the discussion of the different estimators proposed in the literature to detect non-Gaussianity and on outlining the bases of different reconstruction methods that have been applied to the CMB.

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arXiv1999

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.

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arXiv1999

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 $12^{\circ}.8\times 12^{\circ}.8$ 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, $S/N \sim 1$, 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 $C_{\ell}$'s up to $l\sim 1500$ with errors always below $20% $ in cases with $S/N \ge 1$.

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arXiv1998

The effect of point sources on satellite observations of the cosmic microwave background

We study the effect of extragalactic point sources on satellite observations of the cosmic microwave background (CMB). In order to separate the contributions due to different foreground components, a maximum-entropy method is applied to simulated observations by the Planck Surveyor satellite. In addition to point sources, the simulations include emission from the CMB and the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron emission. We find that the main input components are faithfully recovered and, in particular, that the quality of the CMB reconstruction is only slightly reduced by the presence of point sources. In addition, we find that it is possible to recover accurate point source catalogues at each of the Planck Surveyor observing frequencies.

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arXiv1997

Correlation of Excursion Sets for Non-Gaussian CMB Temperature Distributions

We present a method, based on the correlation function of excursion sets above a given threshold, to test the Gaussianity of the CMB temperature fluctuations in the sky. In particular, this method can be applied to discriminate between standard inflationary scenarios and those producing non-Gaussianity such as topological defects. We have obtained the normalized correlation of excursion sets, including different levels of noise, for 2-point probability density functions constructed from the Gaussian, χ_n^2 and Laplace 1-point probability density functions in two different ways. Considering subdegree angular scales, we find that this method can distinguish between different distributions even if the corresponding marginal probability density functions and/or the radiation power spectra are the same.

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arXiv1996

Peaks in the Cosmic Microwave Background: flat versus open models

We present properties of the peaks (maxima) of the CMB anisotropies expected in flat and open CDM models. We obtain analytical expressions of several topological descriptors: mean number of maxima and the probability distribution of the gaussian curvature and the eccentricity of the peaks. These quantities are calculated as functions of the radiation power spectrum, assuming a gaussian distribution of temperature anisotropies. We present results for angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are relevant for the MAP and COBRAS/SAMBA space missions and the ground-based interferometer experiments. Our analysis also includes the effects of noise. We find that the number of peaks can discriminate between standard CDM models, and that the gaussian curvature distribution provides a useful test for these various models, whereas the eccentricity distribution can not distinguish between them.

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