For additive signals on Gaussian clutter, the optimal detector is a linear matched filter that is adapted to the known signal and the covariance of the background. This adaptive matched filter is widely used for gas-phase plume detection, even though the effect of the plume on the background is not strictly additive. Here, a derivation of the matched filter for a strictly absorptive plume produces, in the weak plume limit, a quadratic filter. This quadratic matched filter is extended in two ways: an elliptically-contoured multivariate t distribution is used to generalize the Gaussian background clutter, and a generalized likelihood ratio test detector is derived to extend applicability to stronger plumes. In addition to detectors whose purpose is to identify presence versus absence of a plume, expressions are also derived for estimating plume strength. The performance of these various detectors is evaluated by implanting simulated plume into background images that are either real hyperspectral images or simulated images based on different (Gaussian, multivariate t, and lognormal) clutter distributions.

中文翻译：

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高斯和非高斯背景杂波的吸收性弱羽流检测


对于高斯杂波上的加性信号，最佳检测器是适应已知信号和背景协方差的线性匹配滤波器。这种自适应匹配滤波器广泛用于气相羽流检测，尽管羽流对背景的影响并不是严格相加的。这里，严格吸收羽流的匹配滤波器的推导在弱羽流限制下产生二次滤波器。该二次匹配滤波器以两种方式扩展：使用椭圆形轮廓的多元 t 分布来概括高斯背景杂波，并导出广义似然比测试检测器以将适用性扩展到更强的羽流。除了旨在识别羽流存在与否的探测器之外，还导出了用于估计羽流强度的表达式。这些不同探测器的性能是通过将模拟羽流植入背景图像中来评估的，这些背景图像可以是真实的高光谱图像，也可以是基于不同（高斯、多元 t 和对数正态）杂波分布的模拟图像。