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 localized areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in...

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Bibliographic Details
Published in:Monthly notices of the Royal Astronomical Society 2009-05, Vol.395 (2), p.649-656
Main Authors: Argüeso, F., Sanz, J. L., Herranz, D., López-Caniego, M., González-Nuevo, J.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics
cosmic microwave background
Earth, ocean, space
Estimating techniques
Exact sciences and technology
Mathematical models
methods: data analysis
polarization
radio continuum: galaxies
techniques: image processing
Vector space
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Summary: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 localized 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 pre-filtering 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 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 Jy for (blind/non-blind) detection and in a low noise zone with fluxes Jy for (blind/non-blind) detection with low errors in the estimated flux and position.
ISSN:0035-8711
1365-2966
DOI:10.1111/j.1365-2966.2009.14549.x