Robust Subspace Detectors Based on α -Divergence With Application to Detection in Imaging

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 . 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.