On a nonlocal spectrogram for denoising one-dimensional signals

In previous works, we investigated the use of local filters based on partial differential equations (PDE) to denoise one-dimensional signals through the image processing of time–frequency representations, such as the spectrogram. In these image denoising algorithms, the particularity of the image was hardly taken into account. We turn, in this paper, to study the performance of nonlocal filters, like Neighborhood or Yaroslavsky filters, in the same problem. We show that, for certain iterative schemes involving the Neighborhood filter, the computational time is drastically reduced with respect to Yaroslavsky or nonlinear PDE based filters, while the outputs of the filtering processes are similar. This is heuristically justified by the connection between the fast Neighborhood filter applied to a spectrogram and the corresponding accurate reassigned spectrogram of the image. This correspondence holds only for time–frequency representations of one-dimensional signals, not for usual images, and in this sense the particularity of the image is exploited. We compare through a series of experiments on synthetic and biomedical signals the performance of local and nonlocal filters.