Detection/estimation of the modulus of a vector. Application to point source detection in polarization data

Given a set of images, whose pixel values can be considered as the components of a vector, it is interesting to estimate the modulus of such a vector in some localised areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in a background is relevant in some fields like astrophysics. We develop two different techniques, one based on the Neyman-Pearson lemma, the Neyman-Pearson filter (NPF), and another based on prefiltering-before-fusion, the filtered fusion (FF), to deal with the problem of detection of the source and estimation of the polarization given two or three images corresponding to the different components of polarization (two for linear polarization, three including circular polarization). For the case of linear polarization, we have performed numerical simulations on two-dimensional patches to test these filters following two different approaches (a blind and a non-blind detection), considering extragalactic point sources immersed in cosmic microwave background (CMB) and non-stationary noise with the conditions of the 70 GHz \emph{Planck} channel. The FF outperforms the NPF, especially for low fluxes. We can detect with the FF extragalactic sources in a high noise zone with fluxes >= (0.42,0.36) Jy for (blind/non-blind) detection and in a low noise zone with fluxes >= (0.22,0.18) Jy for (blind/non-blind) detection with low errors in the estimated flux and position.Comment: 11 pages, 5 figure

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.Comment: 10 pages, 2 figures. SPIE Proceedings "Electronic Imaging II", San Jose, CA. January 200

A multifrequency method based on the Matched Multifilter for the detection of point sources in CMB maps

In this work we deal with the problem of simultaneous multifrequency detection of extragalactic point sources in maps of the Cosmic Microwave Background. We apply a linear filtering technique that uses spatial information and the cross-power spectrum. To make this, we simulate realistic and non-realistic flat patches of the sky at two frequencies of Planck: 44 and 100 GHz. We filter to detect and estimate the point sources and compare this technique with the monofrequency matched filter in terms of completeness, reliability, flux and spectral index accuracy. The multifrequency method outperforms the matched filter at the two frequencies and in all the studied cases in the work.Comment: 14 pages, 6 figures, 1 tabl

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.Comment: 12 pages, 6 figures, submitted to MNRA

SAT based Enforcement of Domotic Effects in Smart Environments

The emergence of economically viable and efficient sensor technology provided impetus to the development of smart devices (or appliances). Modern smart environments are equipped with a multitude of smart devices and sensors, aimed at delivering intelligent services to the users of smart environments. The presence of these diverse smart devices has raised a major problem of managing environments. A rising solution to the problem is the modeling of user goals and intentions, and then interacting with the environments using user defined goals. `Domotic Effects' is a user goal modeling framework, which provides Ambient Intelligence (AmI) designers and integrators with an abstract layer that enables the definition of generic goals in a smart environment, in a declarative way, which can be used to design and develop intelligent applications. The high-level nature of domotic effects also allows the residents to program their personal space as they see fit: they can define different achievement criteria for a particular generic goal, e.g., by defining a combination of devices having some particular states, by using domain-specific custom operators. This paper describes an approach for the automatic enforcement of domotic effects in case of the Boolean application domain, suitable for intelligent monitoring and control in domotic environments. Effect enforcement is the ability to determine device configurations that can achieve a set of generic goals (domotic effects). The paper also presents an architecture to implement the enforcement of Boolean domotic effects, and results obtained from carried out experiments prove the feasibility of the proposed approach and highlight the responsiveness of the implemented effect enforcement architectur

Matrix Filters for the Detection of Extragalactic Point Sources in Cosmic Microwave Background Images

In this paper we introduce a new linear filtering technique, the so-called matrix filters, that maximizes the signal-to-interference ratio of compact sources of unknown intensity embedded in a set of images by taking into account the cross-correlations between the different channels. By construction, the new filtering technique outperforms (or at least equals) the standard matched filter applied on individual images. An immediate application is the detection of extragalactic point sources in Cosmic Microwave Background images obtained at different wavelengths. We test the new technique in two simulated cases: a simple two-channel case with ideal correlated color noise and more realistic simulations of the sky as it will be observed by the LFI instrument of the upcoming ESA's Planck mission. In both cases we observe an improvement with respect to the standard matched filter in terms of signal-to-noise interference, number of detections and number of false alarms.Comment: 9 pages, 7 figures, submitted to IEEE Journal of Selected Topics in Signal Processin

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

Polarization of the WMAP Point Sources

The detection of polarized sources in the WMAP 5-year data is a very difficult task. The maps are dominated by instrumental noise and only a handful of sources show up as clear peaks in the Q and U maps. Optimal linear filters applied at the position of known bright sources detect with a high level of significance a polarized flux P from many more sources, but estimates of P are liable to biases. Using a new technique, named the "filtered fusion technique", we have detected in polarization, with a significance level greater than 99.99% in at least one WMAP channel, 22 objects, 5 of which, however, do not have a plausible low radio frequency counterpart and are therefore doubtful. Estimated polarized fluxes P < 400 mJy at 23 GHz were found to be severely affected by the Eddington bias. The corresponding polarized flux limit for Planck/LFI at 30 GHz, obtained via realistic simulations, is 300 mJy. We have also obtained statistical estimates of, or upper limits to the mean polarization degrees of bright WMAP sources at 23, 33, 41, and 61 GHz, finding that they are of a few percent.Comment: 10 pages, 6 figures. Accepted for publication in Ap

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