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

Area of Science:

• Signal processing
• Statistical inference
• Robust statistics

Background:

• Detecting signal subspaces is crucial in various data analysis applications.
• Classical statistical tests can be sensitive to outliers and noise contamination.
• Existing methods may lack adaptability to different noise levels and outlier presence.

Purpose of the Study:

• To develop robust variants of Wald, Rao, and likelihood ratio (LR) tests.
• To enable adjustable trade-offs between test robustness and detection power using a hyperparameter α.
• To provide a unified framework for robust signal detection.

Main Methods:

• Derivation of robust tests using the α-divergence.
• Analysis of asymptotic properties to support the proposed tests.
• Adjustment of robustness and power via a single hyperparameter α.

Main Results:

• Proposed tests demonstrate robustness to outliers, particularly for specific α values.
• Robust LR test shown to be equivalent to the classical LR test or matched subspace detector (MSD) as α approaches 1.
• Numerical experiments validate performance on diverse datasets (fMRI, hyperspectral, SAR).

Conclusions:

• The proposed α-divergence-based tests offer a flexible and robust approach to signal subspace detection.
• These methods provide improved performance in the presence of contaminated Gaussian noise and outliers.
• The adjustable hyperparameter α allows for tailored application across different data types and noise conditions.