用于向量模的检测/估计的滤波器设计。极化数据的应用
Filter Design for the Detection/Estimation of the Modulus of a Vector. Application to Polarization Data
摘要：
我们考虑一组M个图像，其像素在一个共同点的强度可以被视为一个M维向量的分量。我们感兴趣的是这样一个向量的模的估计与一个紧凑的源。例如，沉浸在噪声背景中的紧凑源的偏振信号的检测/估计在诸如天体物理学的某些领域中是相关的。我们开发了两种不同的技术，一种是基于应用于模分布的极大似然估计（MLE）的模滤波器（ModF），另一种是基于融合前对分量进行预滤波的滤波融合（FF）。我们提出了这两种方法在一般情况下的M图像，并将其应用到特定的情况下，三个图像（线性加圆偏振）。数值模拟已经进行了测试这些过滤器考虑极化紧凑源沉浸在平稳的噪声。FF在估计的源的幅度和位置的误差方面比ModF表现得更好，特别是在低信噪比的情况下。我们还比较了这两种方法与直接应用的匹配滤波器（MF）的偏振数据。最后一种技术明显优于新方法。
英文摘要：
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.
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