Data-driven design and complexity control of time-frequency detectors

In this paper, we introduce a method of designing optimal time}frequency detectors from training samples, which is potentially of great bene"t when few a priori information on the nonstationary signal to be detected is available. However, achieving good performance with data-driven detectors requires matching their complexity to the available amount of training samples: receivers with a too large number of adjustable parameters often exhibit a poor generalization performance whereas those with an insu$cient complexity cannot learn all the information available in the design set. Then, using the principle of structural risk minimization proposed by Vapnik, we introduce procedures which provide powerful tools for tuning the complexity of generalized linear detectors and improving their performance. Next, these methods are successfully experimented on simulated and real data, with linear detectors operating in the time}frequency domain: it is in such high-dimensional feature spaces that procedures of deriving reduced-bias receivers from training samples are of prime necessity. Finally, we show that our methodology may o!er a helpful support for designing detectors in many applications of current interest, such as biomedical engineering and complex systems monitoring. ( 1999 Elsevier Science B.V. All rights reserved.