arXiv subjects

J. L. Sanz

Publications and source records attributed to J. L. Sanz.

At least 37 records · Page 2Linked to original sources

arXiv2006

Statistical analysis of undetected point sources in cosmic microwave background maps

Cosmic microwave background (CMB) temperature anisotropies follow a Gaussian statistical distribution in the standard inflationary model, but there are non-Gaussian contributions due to astrophysical foregrounds. The detection of the non-Gaussian signal due to extragalactic point sources and its distinction from the possible intrinsic non-Gaussianity is an issue of great importance in CMB analysis. The Mexican Hat Wavelet Family (MHWF), which has been proved very useful for the detection of extragalactic point sources, is applied here to the study of non-Gaussianity due to point sources in CMB maps. We carry out simulations of CMB maps with the characteristics of the forthcoming Planck mission at 70 and 100 GHz and filter them with the MHWF. By comparing the skewness and kurtosis of simulated maps with and without point sources, we are able to detect clearly the non-Gaussian signal due to point sources for flux limits as low as 0.4 Jy (70 GHz) and 0.3 Jy (100 GHz). The second and third members of the MHWF perform better in this respect than the Mexican Hat Wavelet (MHW1) and much better than the Daubechies 4 wavelet. We have also estimated the third order, $K_3$, and fourth order, $K_4$, cumulants produced by point sources at these Planck channels by means of a fit with the MHWF. The average relative errors with respect to the real values are below 12% for fluxes down to 0.6 Jy (70 GHz) and 0.4 Jy (100 GHz). The values of these cumulants allow us to distinguish between different source counts models.

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arXiv2006

Scalar quantities as detectors of non-Gaussianity on CMB maps

We study the power of several scalar quantities constructed on the sphere (presented in Monteserin et al. 2005) to detect non-Gaussianity on the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractional isotropy, the Laplacian and the shape index. For the kurtosis case, the fractional anisotropy, the Laplacian and the determinant are the quantities that perform better.

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arXiv2006

Comparison of filters for the detection of point sources in Planck simulations

We study the detection of extragalactic point sources in two-dimensional flat simulations for all the frequencies of the forthcoming ESA's Planck mission. In this work we have used the most recent available templates of the microwave sky: as for the diffuse Galactic components and the Sunyaev-Zel'dovich clusters we have used the ``Plank Reference Sky Model''; as for the extragalactic point sources, our simulations - which comprise all the source populations relevant in this frequency interval - are based on up-to-date cosmological evolution models for sources. To consistently compare the capabilities of different filters for the compilation of the - hopefully - most complete blind catalogue of point sources, we have obtained three catalogues by filtering the simulated sky maps with: the Matched Filter (MF), the Mexican Hat Wavelet (MHW1) and the Mexican Hat Wavelet 2 (MHW2), the first two members of the MHW Family. For the nine Planck frequencies we show the number of real and spurious detections and the percentage of spurious detections at different flux detection limits as well as the completeness level of the catalogues and the average errors in the estimation of the flux density of detected sources. Allowing a 5 % of spurious detections, we obtain the following number of detections by filtering with the MHW2 an area equivalent to half of the sky: 580 (30 GHz), 342 (44 GHz), 341 (70 GHz), 730 (100 GHz), 1130 (143 GHz), 1233 (217 GHz), 990 (353 GHz), 1025 (545 GHz) and 3183 (857 GHz). Our current results indicate that the MF and the MHW2 yield similar results, whereas the MHW1 performs worse in some cases and especially at very low fluxes. This is a relevant result, because we are able to obtain comparable results with the well known Matched Filter and with this specific wavelet, the MHW2, which is much easier to implement and use.

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arXiv2006

The Mexican Hat Wavelet Family. Application to point source detection in CMB maps

We propose a new detection technique in the plane based on an isotropic wavelet family. This family is naturally constructed as an extension of the Gaussian-Mexican Hat Wavelet pair and for that reason we call it the Mexican Hat Wavelet Family (MHWF). We show the performance of these wavelets when dealing with the detection of extragalactic point sources in cosmic microwave background (CMB) maps: a very important issue within the most general problem of the component separation of the microwave sky. Specifically, flat two-dimensional simulations of the microwave sky comprising all astrophysical components plus instrumental noise have been analyzed for the channels at 30, 44 and 70 GHz of the forthcoming ESA's Planck mission Low Frequency Instrument (LFI). We adopt up-to-date cosmological evolution models of extragalactic sources able to fit well the new data on high-frequency radio surveys and we discuss our current results on point source detection by comparing them with those obtained using the Mexican Hat Wavelet (MHW) technique, which has been already proven a suitable tool for detecting point sources. By assuming a 5% reliability level, the first new members of the MHWF, at their ``optimal scale'', provide three point source catalogues on half of the sky (at galactic latitude |b|> 30) at 30, 44 and 70 GHz of 639, 387 and 340 extragalactic sources, respectively. The corresponding flux detection limits are 0.38, 0.45 and 0.47 Jy . By using the same simulated sky patches and at the same frequencies as before, the MHW at its optimal scale provides 543, 322 and 311 sources with flux detection limits of 0.44, 0.51 and 0.50 Jy, respectively (5% reliability level). These results show a clear improvement when we use the new members of the MHWF and, in particular, the MHW2 with respect to the MHW.

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arXiv2005

Scalar statistics on the sphere: application to the CMB

A method to compute several scalar quantities of Cosmic Microwave Background maps on the sphere is presented. We consider here four type of scalars: the Hessian matrix scalars, the distortion scalars, the gradient related scalars and the curvature scalars. Such quantities are obtained directly from the spherical harmonic coefficients (alm) of the map. We also study the probability density function of these quantities for the case of a homogeneous and isotropic Gaussian field, which are functions of the power spectrum of the initial field. From these scalars it is posible to construct a new set of scalars which are independent of the power spectrum of the field. We test our results using simulations and find a good agreement between the theoretical probability density functions and those obtained from simulations. Therefore, these quantities are proposed to investigate the presence of non-Gaussian features in CMB maps. Finally, we show how to compute the scalars in presence of anisotropic noise and realistic masks.

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arXiv2005

Some comments on the note "Some comments on the paper 'Filter design for the detection of compact sources based on the Neyman-Pearson detector' by M. Lopez-Caniego et. al (2005, MNRAS 359, 993)" by R. Vio and P. Andreani (astroph/0509394)

In this note we stress the necessity of a careful check of the arguments used by Vio & Andreani (2005) (VA hereinafter) to criticise the superior performance of the biparametric scale adaptive filter (BSAF) with respect to the classic matched filter (MF) in the detection of sources on a random Gaussian background. In particular, we point out that a defective reading and understanding of previous works in the literature (Rice 1954; Barreiro et al. 2003; Lopez-Caniego et al. 2005) leads the authors of VA to the derivation of an incorrect formula and to some misleading conclusions.

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arXiv2005

Filter design for the detection of compact sources based on the Neyman-Pearson detector

This paper considers the problem of compact source detection on a Gaussian background in 1D. Two aspects of this problem are considered: the design of the detector and the filtering of the data. Our detection scheme is based on local maxima and it takes into account not only the amplitude but also the curvature of the maxima. A Neyman-Pearson test is used to define the region of acceptance, that is given by a sufficient linear detector that is independent on the amplitude distribution of the sources. We study how detection can be enhanced by means of linear filters with a scaling parameter and compare some of them (the Mexican Hat wavelet, the matched and the scale-adaptive filters). We introduce a new filter, that depends on two free parameters (biparametric scale-adaptive filter). The value of these two parameters can be determined, given the a priori pdf of the amplitudes of the sources, such that the filter optimizes the performance of the detector in the sense that it gives the maximum number of real detections once fixed the number density of spurious sources. The combination of a detection scheme that includes information on the curvature and a flexible filter that incorporates two free parameters (one of them a scaling) improves significantly the number of detections in some interesting cases. In particular, for the case of weak sources embedded in white noise the improvement with respect to the standard matched filter is of the order of 40%. Finally, an estimation of the amplitude of the source is introduced and it is proven that such an estimator is unbiased and it has maximum efficiency. We perform numerical simulations to test these theoretical ideas and conclude that the results of the simulations agree with the analytical ones.

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arXiv2005

A Bayesian approach to filter design: detection of compact sources

We consider filters for the detection and extraction of compact sources on a background. We make a one-dimensional treatment (though a generalization to two or more dimensions is possible) assuming that the sources have a Gaussian profile whereas the background is modeled by an homogeneous and isotropic Gaussian random field, characterized by a scale-free power spectrum. Local peak detection is used after filtering. Then, a Bayesian Generalized Neyman-Pearson test is used to define the region of acceptance that includes not only the amplification but also the curvature of the sources and the a priori probability distribution function of the sources. We search for an optimal filter between a family of Matched-type filters (MTF) modifying the filtering scale such that it gives the maximum number of real detections once fixed the number density of spurious sources. We have performed numerical simulations to test theoretical ideas.

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arXiv2005

Detection of point sources on two-dimensional images based on peaks

This article considers the detection of point sources in two dimensional astronomical images. The detection scheme we propose is based on peak statistics. We discuss the example of the detection of far galaxies in Cosmic Microwave Background experiments throughout the paper, although the method we present is totally general and can be used in many other fields of data analysis. We assume sources with a Gaussian profile --that is a fair approximation of the profile of a point source convolved with the detector beam in microwave experiments-- on a background modeled by a homogeneous and isotropic Gaussian random field characterized by a scale-free power spectrum. Point sources are enhanced with respect to the background by means of linear filters. After filtering, we identify local maxima and apply our detection scheme, a Neyman-Pearson detector that defines our region of acceptance based on the a priori pdf of the sources and the ratio of number densities. We study the different performances of some linear filters that have been used in this context in the literature: the Mexican Hat wavelet, the matched filter and the scale-adaptive filter. We consider as well an extension to two dimensions of the biparametric scale adaptive filter (BSAF). The BSAF depends on two parameters which are determined by maximizing the number density of real detections while fixing the number density of spurious detections. For our detection criterion the BSAF outperforms the other filters in the interesting case of white noise.

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arXiv2004

Gaussianity of the CMB: Smooth Goodness of Fit Tests Applied to Interferometric Data

We adapt the smooth tests of goodness of fit developed by Rayner and Best to the study of the non-Gaussianity of interferometric observations of the cosmic microwave background (CMB). The interferometric measurements (visibilities) are transformed into signal-to-noise eigenmodes, and then the method is applied directly in Fourier space. This transformation allows us to perform the analysis in different subsets of eigenmodes according to their signal-to-noise level. The method can also deal with non-uniform or incomplete coverage of the UV plane. We explore here two possibilities: we analyse either the real and imaginary parts of the complex visibilities (Gaussianly distributed under the Gaussianity hypothesis) or their phases (uniformly distributed under the Gaussianity hypothesis). The power of the method in discriminating between Gaussian and non-Gaussian distributions is studied by using several kinds of non-Gaussian simulations. On the one hand, we introduce a certain degree of non-Gaussianity directly into the Fourier space using the Edgeworth expansion, and afterwards the desired correlation is introduced. On the other hand, we consider interferometric observations of a map with topological defects (cosmic strings). To these previous non-Gaussian simulations we add different noise levels and quantify the required signal-to-noise ratio necessary to achieve a detection of these non-Gaussian features. Finally, we have also studied the ability of the method to constrain the so-called nonlinear coupling constant f_{NL} using chi^2 simulations.The whole method is illustrated here by application to simulated data from the Very Small Array interferometer.

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arXiv2004

The estimation of the SZ effects with unbiased multifilters

In this work we study the performance of linear multifilters for the estimation of the amplitudes of the thermal and kinematic Sunyaev-Zel'dovich effects. We show that when both effects are present, estimation of these effects with standard matched multifilters is intrinsically biased. This bias is due to the fact that both signals have basically the same spatial profile. We find a new family of multifilters related to the matched multifilters that cancel this systematic bias, hence we call them Unbiased Matched Multifilters. We test the unbiased matched multifilters and compare them with the standard matched multifilters using simulations that reproduce the future Planck mission's observations. We find that in the case of the standard matched multifilters the systematic bias in the estimation of the kinematic Sunyaev-Zel'dovich effect can be very large, even greater than the statistical error bars. Unbiased matched multifilters cancel effectively this kind of bias. In concordance with other works in the literature, our results indicate that the sensitivity and resolution of Planck will not be enough to give reliable estimations of the kinematic Sunyaev-Zel'dovich of individual clusters. However, since the estimation with the unbiased matched multifilters is not intrinsically biased, it can be possible to use them to statistically study peculiar velocities in large scales using large sets of clusters.

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arXiv2004

Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets

A non-Gaussian detection in the WMAP 1-year data is reported. The detection has been found in the combined Q-V-W map proposed by the WMAP team (Komatsu et al. 2003) after applying a wavelet technique based on the Spherical Mexican Hat Wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales. A non-Gaussian signal is detected at scales of the SMHW around 4 deg (size in the sky of around 10 deg). The right tail probability of the detection is approx. 0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right tail probability of approx. 0.1%. Systematics, foregrounds and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: 1) each one of the Q, V and W receivers shows the same non-Gaussianity pattern, and 2) several combinations of the different receivers at each frequency band do not show this non-Gaussian pattern. Similarly, galactic foregrounds show a negligible contribution to the non-Gaussian detection: non-Gaussianity is detected in all the WMAP maps and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behaviour compatible with the Gaussian model. Influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (like secondary anisotropies and primordial features) can not be rejected as the source of this non-Gaussian detection.

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arXiv2003

Tests of Gaussianity

We review two powerful methods to test the Gaussianity of the cosmic microwave background (CMB): one based on the distribution of spherical wavelet coefficients and the other on smooth tests of goodness-of-fit. The spherical wavelet families proposed to analyse the CMB are the Haar and the Mexican Hat ones. The latter is preferred for detecting non-Gaussian homogeneous and isotropic primordial models containing some amount of skewness or kurtosis. Smooth tests of goodness-of-fit have recently been introduced in the field showing some interesting properties. We will discuss the smooth tests of goodness-of-fit developed by Rayner and Best for the univariate as well as for the multivariate analysis.

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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

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.

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arXiv2003

Point Source Detection using the Spherical Mexican Hat Wavelet on simulated all-sky Planck maps

We present an estimation of the point source (PS) catalogue that could be extracted from the forthcoming ESA Planck mission data. We have applied the Spherical Mexican Hat Wavelet (SMHW) to simulated all-sky maps that include CMB, Galactic emission (thermal dust, free-free and synchrotron), thermal Sunyaev-Zel'dovich effect and PS emission, as well as instrumental white noise. This work is an extension of the one presented in Vielva et al. (2001a). We have developed an algorithm focused on a fast local optimal scale determination, that is crucial to achieve a PS catalogue with a large number of detections and a low flux limit. An important effort has been also done to reduce the CPU time processor for spherical harmonic transformation, in order to perform the PS detection in a reasonable time. The presented algorithm is able to provide a PS catalogue above fluxes: 0.48 Jy (857 GHz), 0.49 Jy (545 GHz), 0.18 Jy (353 GHz), 0.12 Jy (217 GHz), 0.13 Jy (143 GHz), 0.16 Jy (100 GHz HFI), 0.19 Jy (100 GHz LFI), 0.24 Jy (70 GHz), 0.25 Jy (44 GHz) and 0.23 Jy (30 GHz). We detect around 27700 PS at the highest frequency Planck channel and 2900 at the 30 GHz one. The completeness level are: 70% (857 GHz), 75% (545 GHz), 70% (353 GHz), 80% (217 GHz), 90% (143 GHz), 85% (100 GHz HFI), 80% (100 GHz LFI), 80% (70 GHz), 85% (44 GHz) and 80% (30 GHz). In addition, we can find several PS at different channels, allowing the study of the spectral behaviour and the physical processes acting on them. We also present the basic procedure to apply the method in maps convolved with asymmetric beams. The algorithm takes ~ 72 hours for the most CPU time demanding channel (857 GHz) in a Compaq HPC320 (Alpha EV68 1 GHz processor) and requires 4 GB of RAM memory.

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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

A Bayesian non-parametric method to detect clusters in Planck data

We show how one may expect a significant number of SZ detections in future Planck data without any of the typical assumptions needed in present component separation methods, such as about the power spectrum or the frequency dependence of any of the components, circular symmetry or a typical scale for the clusters. We reduce the background by subtracting an estimate of the point sources, dust and CMB. The final SZE map is estimated in Fourier space. The catalogue of returned clusters is complete above flux 200 mJy (353 GHz) while the lowest flux reached by our method is about 70 mJy (353 GHz). We predict a large number of detections (about 9000) in 4/5 of the sky. This large number of SZ detections will allow a robust and consistent analysis of the evolution of the cluster population with redshift and will have important implications for determining the best cosmological model.

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