CHARACTERIZATION OF SIGNALSBY THE RIDGES OF THEIR WAVELETTRANSFORMSRen

Many procedures have been developed to characterize a signal by some of the salient features of a speciic transform, whether it is the Fourier, the Gabor, the Wigner or more recently the wavelet transform. Ridges in the modulus of the transform determine regions in the transform domain with a high concentration of energy. For this reason they are regarded as natural candidates for the characterization and the reconstruction of the original signal. We present a couple of new algorithmic procedures for the detection of ridges in the modulus of the (continuous) wavelet transform of one-dimensional signals. These detection procedures are shown to be robust to additive noise. We also derive and test a new reconstruction procedure. The latter uses only information of the restriction of the wavelet transform to a sample of points from the ridge. This provides with a very eecient way to code the information contained in the signal.