Wolf population counting by spectrogram image processing

We investigate the use of image processing techniques based on partial differential equations applied to the image produced by time-frequency representations of one-dimensional signals, such as the spectrogram. Specifically, we use the PDE model introduced by Álvarez, Lions and Morel for noise smoothing and edge enhancement, which we show to be stable under signal and window perturbations in the spectrogram image. We demonstrate by numerical examples that the corresponding numerical algorithm applied on the spectrogram of a noisy signal reduces the noise and produce an enhancement of the instantaneous frequency lines, allowing to track this lines more accurately than with the original spectrogram. We apply this technique both for synthetic signals and for wolves chorus field recorded signals, which was the original motivation of this work.