Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the $\alpha -$ divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter $\alpha $ . It is shown that when $\alpha \rightarrow 1$ , these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of $\alpha < 1$ . Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented.

中文翻译：

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基于鲁棒性的子空间检测器 α散度及其在成像检测中的应用

本文提出了鲁棒的Wald，Rao和似然比（LR）测试方法，用于检测受污染的高斯噪声破坏的信号干扰子空间中的信号子空间。它们是使用 $ \ alpha-$ 差异，并且可以使用单个超参数来调整测试的鲁棒性和功效（检测概率）之间的权衡 $ \ alpha $ 。结果表明，当 $ \ alpha \ rightarrow 1 $ ，这些测试等同于众所周知的经典测试。例如，鲁棒的LR测试与LR测试或匹配的子空间检测器（MSD）一致。提供渐近结果以支持建议的测试，并使用的值获得对异常值的鲁棒性 $ \ alpha <1 $ 。还提供了数值实验，说明了这些测试在模拟的，实际的功能磁共振成像（fMRI），高光谱和合成孔径雷达（SAR）数据上的性能。