Some Good Reasons to Use Matched Filters for the Detection of Point Sources in CMB Maps

In this draft we comment on the results concerning the performances of matched filters, scale adaptive filters and Mexican hat wavelet that recently appeared in literature in the context of point source detection in Cosmic Microwave Background maps. In particular, we show that, contrary to what has been claimed, the use of the matched filters still appear to be the most reliable and efficient method to disantangle point sources from the backgrounds, even when using detection criterion that, differently from the classic $n\sigma$ thresholding rule, takes into account not only the height of the peaks in the signal corresponding to the candidate sources but also their curvature.Comment: Replacement after submission to A&A and referee's comments. Astronomy and Astrophysics, in press, JNL/2003/473

Statistical properties of dust far-infrared emission

The description of the statistical properties of dust emission gives important constraints on the physics of the interstellar medium but it is also a useful way to estimate the contamination of diffuse interstellar emission in the cases where it is considered a nuisance. The main goals of this analysis of the power spectrum and non-Gaussian properties of 100 micron dust emission are 1) to estimate the power spectrum of interstellar matter density in three dimensions, 2) to review and extend previous estimates of the cirrus noise due to dust emission and 3) to produce simulated dust emission maps that reproduce the observed statistical properties. The main results are the following. 1) The cirrus noise level as a function of brightness has been previously overestimated. It is found to be proportional to instead of ^1.5, where is the local average brightness at 100 micron. This scaling is in accordance with the fact that the brightness fluctuation level observed at a given angular scale on the sky is the sum of fluctuations of increasing amplitude with distance on the line of sight. 2) The spectral index of dust emission at scales between 5 arcmin and 12.5 degrees is =-2.9 on average but shows significant variations over the sky. Bright regions have systematically steeper power spectra than diffuse regions. 3) The skewness and kurtosis of brightness fluctuations is high, indicative of strong non-Gaussianity. 4) Based on our characterization of the 100 micron power spectrum we provide a prescription of the cirrus confusion noise as a function of wavelength and scale. 5) Finally we present a method based on a modification of Gaussian random fields to produce simulations of dust maps which reproduce the power spectrum and non-Gaussian properties of interstellar dust emission.Comment: 13 pages, 13 figures. Accepted for publication in A&

On Optimal Detection of Point Sources in CMB Maps

Point-source contamination in high-precision Cosmic Microwave Background (CMB) maps severely affects the precision of cosmological parameter estimates. Among the methods that have been proposed for source detection, wavelet techniques based on ``optimal'' filters have been proposed.In this paper we show that these filters are in fact only restrictive cases of a more general class of matched filters that optimize signal-to-noise ratio and that have, in general, better source detection capabilities, especially for lower amplitude sources. These conclusions are confirmed by some numerical experiments. \keywords{Methods: data analysis -- Methods: statisticalComment: 6 pages, 3 figure

The correct estimate of the probability of false detection of the matched filter in the detection of weak signals. II. (Further results with application to a set of ALMA and ATCA data)

The matched filter (MF) is one of the most popular and reliable techniques to the detect signals of known structure and amplitude smaller than the level of the contaminating noise. Under the assumption of stationary Gaussian noise, MF maximizes the probability of detection subject to a constant probability of false detection or false alarm (PFA). This property relies upon a priori knowledge of the position of the searched signals, which is usually not available. Recently, it has been shown that when applied in its standard form, MF may severely underestimate the PFA. As a consequence the statistical significance of features that belong to noise is overestimated and the resulting detections are actually spurious. For this reason, an alternative method of computing the PFA has been proposed that is based on the probability density function (PDF) of the peaks of an isotropic Gaussian random field. In this paper we further develop this method. In particular, we discuss the statistical meaning of the PFA and show that, although useful as a preliminary step in a detection procedure, it is not able to quantify the actual reliability of a specific detection. For this reason, a new quantity is introduced called the specific probability of false alarm (SPFA), which is able to carry out this computation. We show how this method works in targeted simulations and apply it to a few interferometric maps taken with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Australia Telescope Compact Array (ATCA). We select a few potential new point sources and assign an accurate detection reliability to these sources.Comment: 28 pages, 20 figures, Astronomy & Astrophysics, Minor changes and some typos correcte

Unevenly-sampled signals: a general formalism of the Lomb-Scargle periodogram

The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a component other than noise, when a peak in the periodogram exceeds it. In the case of signals sampled on a regular time grid, determination of such a threshold is relatively simple. When the sampling is uneven, however, things are more complicated. The most popular solution in this case is to use the "Lomb-Scargle" periodogram, but this method can be used only when the noise is the realization of a zero-mean, white (i.e. flat-spectrum) random process. In this paper, we present a general formalism based on matrix algebra, which permits analysis of the statistical properties of a periodogram independently of the characteristics of noise (e.g. colored and/or non-stationary), as well as the characteristics of sampling.Comment: 10 pages, 11 figures, Astronomy and Astrophysics, in pres

Ly-alpha forest: efficient unbiased estimation of second-order properties with missing data

Context. One important step in the statistical analysis of the Ly-alpha forest data is the study of their second order properties. Usually, this is accomplished by means of the two-point correlation function or, alternatively, the K-function. In the computation of these functions it is necessary to take into account the presence of strong metal line complexes and strong Ly-alpha lines that can hidden part of the Ly-alpha forest and represent a non negligible source of bias. Aims. In this work, we show quantitatively what are the effects of the gaps introduced in the spectrum by the strong lines if they are not properly accounted for in the computation of the correlation properties. We propose a geometric method which is able to solve this problem and is computationally more efficient than the Monte Carlo (MC) technique that is typically adopted in Cosmology studies. The method is implemented in two different algorithms. The first one permits to obtain exact results, whereas the second one provides approximated results but is computationally very efficient. The proposed approach can be easily extended to deal with the case of two or more lists of lines that have to be analyzed at the same time. Methods. Numerical experiments are presented that illustrate the consequences to neglect the effects due to the strong lines and the excellent performances of the proposed approach. Results. The proposed method is able to remarkably improve the estimates of both the two-point correlation function and the K-function.Comment: A&A accepted, 12 pages, 15 figure