Structural risk minimization for reduced-bias time-frequency-based detectors design

Detectors design requires substantial knowledge of the observation statistical properties, conditionally to the competing hypotheses H₀ and H₁. However, many applications involve complex phenomena, in which few a priori information is available. Several methods of designing time-frequency-based (TF) receivers from labeled training data have been proposed. Unfortunately, the resulting detectors have large biases, particularly when the number of training samples is small compared to the data dimension. The method presented is based on the structural risk minimization principle developed by Vapnik (1982), and consists in locally adjusting the resolution of TF-based detectors to the information carried by each TF location. This operation, controlled by a measure of H₀ and H₁ separability, allows one to advantageously reduce the receivers complexity and solutions bias. The resulting reduced-bias TF-based detectors can yield a substantial improvement in detection performance