arXiv subjects

Roberto Vio

Publications and source records attributed to Roberto Vio.

10 recordsLinked to original sources

arXiv2021

Everything you always wanted to know about matched filters (but were afraid to ask)

In this paper we review the application of the matched filter (MF) technique and its application to detect weak, deterministic, smooth signals in a stationary, random, Gaussian noise. This is particular suitable in astronomy to detect emission lines in spectra and point-sources in two-dimensional maps. A detailed theoretical development is already available in many books (e.g. Kay 1998; Poor 1994; McNicol 2005; Hippenstiel 2002; Macmillan & Creelma 2005; Wickens 2002; Barkat 2005; Tuzlukov 2001; Levy 2008). Our aim is to examine some practical issues that are typically ignored in textbooks or even in specialized literature as, for example, the effects of the discretization of the signals and the non-Gaussian nature of the noise. To this goal we present each item in the form of answers to specific questions. The relative mathematics and its demonstration are kept to a bare simplest minimum, in the hope of a better understanding of the real performances of the MF in practical applications. For the ease of formalism, arguments will be developed for one-dimensional signals. The extension to the two-dimensional signals is trivial and will be highlighted in dedicated sections.

astro-ph.IM↗

arXiv2020

Modeling high-dimensional dependence among astronomical data

Fixing the relationship of a set of experimental quantities is a fundamental issue in many scientific disciplines. In the 2D case, the classical approach is to compute the linear correlation coefficient from a scatterplot. This method, however, implicitly assumes a linear relationship between the variables. Such an assumption is not always correct. With the use of the partial correlation coefficients, an extension to the multidimensional case is possible. However, the problem of the assumed mutual linear relationship of the variables remains. A relatively recent approach that makes it possible to avoid this problem is the modeling of the joint probability density function (PDF) of the data with copulas. These are functions that contain all the information on the relationship between two random variables. Although in principle this approach also can work with multidimensional data, theoretical as well computational difficulties often limit its use to the 2D case. In this paper, we consider an approach based on so-called vine copulas, which overcomes this limitation and at the same time is amenable to a theoretical treatment and feasible from the computational point of view. We applied this method to published data on the near-IR and far-IR luminosities and atomic and molecular masses of the Herschel reference sample, a volume-limited sample in the nearby Universe. We determined the relationship of the luminosities and gas masses and show that the far-IR luminosity can be considered as the key parameter relating the other three quantities. Once removed from the 4D relation, the residual relation among the latter is negligible. This may be interpreted as the correlation between the gas masses and near-IR luminosity being driven by the far-IR luminosity, likely by the star formation activity of the galaxy.

stat.ME↗

arXiv2018

Matched filter in the low-number count Poisson noise regime: an efficient and effective implementation

The matched filter (MF) is widely used to detect signals hidden within the noise. If the noise is Gaussian, its performances are well-known and describable in an elegant analytical form. The treatment of non-Gaussian noises is often cumbersome as in most cases there is no analytical framework. This is true also for Poisson noise which, especially in the low-number count regime, presents the additional difficulty to be discrete. For this reason in the past methods have been proposed based on heuristic or semi-heuristic arguments. Recently, an analytical form of the MF has been introduced but the computation of the probability of false detection or false alarm (PFA) is based on numerical simulations. To overcome this inefficient and time consuming approach we propose here an effective method to compute the PFA based on the saddle point approximation (SA). We provide the theoretical framework and support our findings by means of numerical simulations. We discuss also the limitations of the MF in practical applications.

astro-ph.IM↗

arXiv2017

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.

astro-ph.IM↗

arXiv2016

On the Correct Estimate of the Probability of False Detection of the Matched Filter in Weak-Signal Detection Problems

The detection reliability of weak signals is a critical issue in many astronomical contexts and may have severe consequences for determining number counts and luminosity functions, but also for optimising the use of telescope time in follow-up observations. Because of its optimal properties, one of the most popular and widely-used detection technique is the matched filter (MF). This is a linear filter designed to maximise the detectability of a signal of known structure that is buried in additive Gaussian random noise. In this work we show that in the very common situation where the number and position of the searched signals within a data sequence (e.g. an emission line in a spectrum) or an image (e.g. a point-source in an interferometric map) are unknown, this technique, when applied in its standard form, may severely underestimate the probability of false detection. This is because the correct use of the MF relies upon a-priori knowledge of the position of the signal of interest. In the absence of this information, the statistical significance of features that are actually noise is overestimated and detections claimed that are actually spurious. For this reason, we present an alternative method of computing the probability of false detection that is based on the probability density function (PDF) of the peaks of a random field. It is able to provide a correct estimate of the probability of false detection for the one-, two- and three-dimensional case. We apply this technique to a real two-dimensional interferometric map obtained with ALMA.

astro-ph.IM↗

arXiv2011

Detection of new point-sources in WMAP Cosmic Microwave Background (CMB) maps at high Galactic latitude. A new technique to extract point sources from CMB maps

In experimental microwave maps, point-sources can strongly affect the estimation of the power-spectrum and/or the test of Gaussianity of the Cosmic Microwave Background (CMB) component. As a consequence, their removal from the sky maps represents a critical step in the analysis of the CMB data. Before removing a source, however, it is necessary to detect it and source extraction consists of a delicate preliminary operation. In the literature, various techniques have been presented to detect point-sources in the sky maps. The most sophisticated ones exploit the multi-frequency nature of the observations that is typical of the CMB experiments. These techniques have "optimal" theoretical properties and, at least in principle, are capable of remarkable performances. Actually, they are rather difficult to use and this deteriorates the quality of the obtainable results. In this paper, we present a new technique, the "weighted matched filter" (WMF), that is quite simple to use and hence more robust in practical applications. Such technique shows particular efficiency in the detection of sources whose spectra have a slope different from zero. We apply this method to three Southern Hemisphere sky regions - each with an area of 400 square degrees - of the seven years Wilkinson Microwave Anisotropy Probe (WMAP) maps and compare the resulting sources with those of the two seven-year WMAP point-sources catalogues. In these selected regions we find seven additional sources not previously listed in WMAP catalogues and discuss their most likely identification and spectral properties.

astro-ph.CO↗

arXiv2006

Comments on the paper "The Mexican Hat Wavelet Family. Application to point source detection in CMB maps" by J. Gonzalez-Nuevo et al. (astro-ph/0604376)

The arguments presented by Gonzalez-Nuevo et. al (2006) in favour of the Mexican Hat Wavelet Family (MHWF) are critically discussed here. These authors allege the optimal properties of this new class of filters in the detection of point sources embedded in a noise background but their claim is not based upon a solid mathematical foundation and proof.

astro-ph↗

arXiv2003

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 $nσ$ thresholding rule, takes into account not only the height of the peaks in the signal corresponding to the candidate sources but also their curvature.

astro-ph↗

arXiv2001

Numerical Simulation of Non-Gaussian Random Fields with Prescribed Correlation Structure

In this paper we will consider the problem of the numerical simulation of non-Gaussian, scalar random fields with a prescribed correlation structure provided either by a theoretical model or computed on a set of observational data. Although, the numerical generation of a generic, non-Gaussian random field is a trivial operation, the task becomes tough when constraining the field with a prefixed correlation structure. At this regards, three numerical methods, useful for astronomical applications, are presented. The limits and capabilities of each method are discussed and the pseudo-codes describing the numerical implementation are provided for two of them.

astro-ph↗

arXiv1997

The Nature of the Broad--Line--Region in the Radio--Loud AGN 3C390.3

We present an analysis of the ultraviolet and X-Ray variability of the Broad- Line-Radio Galaxy 3C390.3 over 15 years. The UV continuum showed large variations with amplitudes of up to a factor of 10. We find: (1) The variations of CIV and Ly_alpha are highly correlated with the UV continuum, and are delayed with respect to the continuum variations by 50-110 days with the red wing of both CIV and Ly_alpha , leading the blue wing; (2) The CIV/Ly_alpha ratio is positively correlated with both the continuum flux and UV line strength, a behavior different from other AGNs studied so far; (3) The blue sides of the Ly_alpha and CIV profiles are similar to the blue side of the Balmer lines, while the red sides are different, suggesting a different origin for the red peak in the Balmer lines. Our results suggest: (1) The broad CIV and Ly_alpha emitting gas is infalling towards the central object; (2) The overall behaviour of the CIV/Ly_alpha ratio and the absence of a big blue bump, strongly indicate the coexistence of optically thick as well as optically thin BLR clouds; (3) Assuming circular symmetry and predominantly circular motion, the BLR gas is situated at 83$\pm$25 lightdays from the central source; (4) Under these assumptions and with the derived circular velocity of $v_{rot} \simeq$ 2850 km s$^{-1}$, the central mass inside this radius is confined to $1.3~10^8 M\odot < M_{CM}< 4.0~10^8 M\odot$; (6) Comparing our results with those obtained from VLBI and observations of the Fe $Kα$ line, suggests the association of the BLR with a disk, inclined at 98$\pm$12 degrees with respect to the direction of superluminal motion of the radio blobs.

astro-ph↗