Multiridge detection and time-frequency reconstruction

The ridges of the wavelet transform, the Gabor transform, or any time-frequ ency representation of a signal contain crucial information on the characte ristics 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 especially adapted to the present situation. We show that this detection algorithm is especially useful for noisy signals with multiridge transforms. It is a common practic e among practitioners to reconstruct a signal from the skeleton of a transf orm of the signal (i.e., the restriction of the transform to the ridges.) A fter reviewing several known procedures, we introduce a new reconstruction algorithm, and we illustrate its efficiency on speech signals and its robus tness and stability on chirps perturbed by synthetic noises at different SN R's.