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We present two robust detectors for nonstationary random signals that belong to p-point uncertainty classes, one being based on an estimator-correlator approach, the other using the deflection criterion. Apart from stable performance, these robust detectors have the advantage of requiring only reduced prior knowledge. Using local cosine bases, we provide an intuitive and highly efficient time-frequency implementation of these robust detectors along with an extension that permits signal-adaptive operation. Simulation results illustrate the robustness of the proposed detectors.