向量模的检测/估计。极化数据点源检测的应用
Detection/estimation of the modulus of a vector. Application to point source detection in polarization data
摘要：
给定一组图像，其像素值可以被认为是矢量的分量，在对应于紧凑信号的一些局部区域中估计这样的矢量的模是有趣的。例如，浸没在背景中的紧凑源中的偏振信号的检测/估计在诸如天体物理学的一些领域中是相关的。我们开发了两种不同的技术，一种是基于奈曼-皮尔逊引理，奈曼-皮尔逊滤波器（NPF），另一种是基于预滤波前融合，滤波融合（FF），以处理的问题的检测源和估计的偏振给定的两个或三个图像对应于不同的偏振分量（两个线性偏振，三个包括圆偏振）。对于线性极化的情况下，我们已经进行了数值模拟的二维补丁测试这些过滤器以下两种不同的方法（盲和非盲检测），考虑河外点源浸没在宇宙微波背景（CMB）和非平稳噪声的条件下的70 GHz的\emph{Planck}通道。FF的性能优于NPF，特别是在低通量时。我们可以检测与FF河外源在一个高噪声区与流量>=（0.42，0.36）Jy（盲/非盲）检测和在一个低噪声区与流量>=（0.22，0.18）Jy（盲/非盲）检测与估计的流量和位置的低误差。
英文摘要：
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.
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