Multi-Ridge Detection and Time-Frequency Reconstruction

Overview & Synopsis

The ridges of the wavelet transform, the Gabor transform or any time-frequency representation of a signal contain crucial information on the characteristics of the signal. Indeed they mark the regions of the time-frequency plane where the signal concentrates most of its energy. We introduce a new algorithm to detect and identify these ridges. The procedure is based on an original form of Markov Chain Monte Carlo algorithm specially adapted to the present situation. We show that this detection algorithm is especially useful for noisy signals with multi-ridge transforms. It is a common practice among practitioners to reconstruct a signal from the skeleton of a transform of the signal (i.e. the restriction of the transform to the ridges). After reviewing several known procedures we introduce a new reconstruction algorithm and we illustrate its efficiency on speech signals.