论文标题
用椭圆形的$ t $分布的高光谱成像中的子像素检测
Sub-pixel detection in hyperspectral imaging with elliptically contoured $t$-distributed background
论文作者
论文摘要
当该目标仅占用像素的一小部分时，检测具有已知光谱特征的目标是高光谱成像中的重要问题。我们最近为这种子像素靶标而得出了广义的似然比检验（GLRT），要么是针对所谓的替换模型，因此，由于相当于一个等于一个的丰度，目标的存在会诱导背景功率的降低，或者对于一个减轻了替代模型的某些限制的混合模型。在这两种情况下，都假定背景为高斯分布。这种简短的交流的目的是将这些检测器扩展到更广泛的椭圆形轮廓分布类别，更确切地说是具有未知均值和协方差矩阵的矩阵变差$ t $分布。我们表明，在$ t $分布式的案例中，广义的似然比测试与其高斯对应物一致，这使后者的应用程序增加了一般性。这些检测器的性能以及鲁棒性通过数值模拟进行评估。
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.
