Implementation of a diffusive differential reassignment method for signal enhancement: An application to wolf population counting

摘要

We investigate the combination of two PDE-based image processing techniques applied to the image produced by time-frequency representations of one-dimensional signals, such as the spectrogram. Specifically, we consider the energy transport equation associated to the lagrangian coordinates corresponding to the spectrogram differential reassignment proposed by Chassandre-Mottin, Daubechies, Auger and Flandrin as a spectrogram readability improving method, together with the image restoration model proposed by Álvarez, Lions and Morel for noise reduction and edge enhancement. Our aim is to produce a transformation of the spectrogram in which the instantaneous frequency lines are easier to track, for using it as an input for a (wolves howls) counting algorithm.After presenting the model derivation, we show some analytical properties of it, such as the existence of a unique solution and a comparison principle, and perform later a discretization to numerically investigate its performance for the cases of synthetic signals and field recorded wolves choruses. We finally compare our results with those obtained from well-established techniques.