Detection of a target with known spectral signature when this target may occupy only a fraction of the pixel is an important issue in hyperspectral imaging. We recently derived the generalized likelihood ratio test (GLRT) for such sub-pixel targets, either for the so-called replacement model where the presence of a target induces a decrease of the background power, due to the sum of abundances equal to one, or for a mixed model which alleviates some of the limitations of the replacement model. In both cases, the background was assumed to be Gaussian distributed. The aim of this short communication is to extend these detectors to the broader class of elliptically contoured distributions, more precisely matrix-variate $t$-distributions with unknown mean and covariance matrix. We show that the generalized likelihood ratio tests in the $t$-distributed case coincide with their Gaussian counterparts, which confers the latter an increased generality for application. The performance as well as the robustness of these detectors are evaluated through numerical simulations.

中文翻译：

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具有椭圆轮廓 t 分布背景的高光谱成像中的亚像素检测

当目标可能只占据像素的一小部分时，检测具有已知光谱特征的目标是高光谱成像中的一个重要问题。我们最近为这些子像素目标推导出了广义似然比检验 (GLRT)，或者针对所谓的替换模型，其中目标的存在会导致背景功率降低，因为丰度之和等于 1，或用于减轻替换模型的某些限制的混合模型。在这两种情况下，背景都被假定为高斯分布。这个简短的交流的目的是将这些检测器扩展到更广泛的椭圆轮廓分布，更准确地说是具有未知均值和协方差矩阵的矩阵变量 $t$-分布。我们表明，$t$-distributed 情况下的广义似然比检验与其高斯对应物一致，这使后者具有更高的应用通用性。这些检测器的性能和稳健性通过数值模拟进行评估。