Multiridge detection and time-frequency reconstruction

TLDR

Ridges in time‑frequency representations such as wavelet or Gabor transforms highlight where a signal concentrates most of its energy and are widely used to reconstruct signals from the transform skeleton. The study introduces a new algorithm to detect and identify ridges in time‑frequency representations. The algorithm employs a tailored Markov chain Monte Carlo approach and includes a reconstruction method that is efficient for speech signals and robust to chirps corrupted by synthetic noise at varying SNRs. The detection algorithm proves especially effective for noisy signals with multiridge transforms, and the reconstruction method demonstrates efficiency on speech signals and robustness on chirps with synthetic noise across different SNRs.

Abstract

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 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 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 and its robustness and stability on chirps perturbed by synthetic noise at different SNRs.