Transient signal detection using overcomplete wavelet transform and high-order statistics

We consider the problem of transient signal detection, followed by a virtual characterization stage. There are two main difficulties which appear in this field. The first one is due to the noise which acts in a real environment. Secondly, when we are interested in signal characterization, it is important to provide more complete information about its time-frequency behavior. Consequently, we propose an adaptive time-frequency method based on the overcomplete wavelet transform concept, in which case an irregular sampling procedure is involved. This procedure uses a method based on the fourth order moment, applied for each sub-band, in order to establish the optimal weight for each sample. The results obtained for real data prove the capability of the proposed approach to detect a transient signal accurately, compared with some classical methods (spectrogram or standard wavelet transform, for example).