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

TL;DR

This paper introduces two new techniques for detecting and estimating the polarization modulus of sources in images, demonstrating their effectiveness in astrophysical data with low flux sources.

Contribution

It develops and compares the Neyman-Pearson filter and filtered fusion methods for polarization source detection, showing FF's superior performance in noisy conditions.

Findings

Filtered fusion outperforms Neyman-Pearson filter in low flux detection.

Detection thresholds are as low as 0.18 Jy in low noise zones.

High accuracy in flux and position estimation for detected sources.

Abstract

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.