  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
this image denoising algorithms, the particularity of the image was hardly
taken into account. We turn, in this paper, to study the performance of
non-local 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 Nonlocal Means filter (accurate) applied to the Wigner-Ville
distribution of the signal. This correspondence holds only for time-frequency
representations of one-dimensional signals, not to usual images, and in this
sense the particularity of the image is exploited. We compare though a series
of experiments on synthetic and biomedical signals the performance of local and
non-local filters.
