On a non-local spectrogram for denoising one-dimensional signals

TL;DR

This paper explores the use of non-local filters, such as Neighborhood filters, for denoising one-dimensional signals via spectrograms, achieving similar quality to nonlinear PDE filters but with significantly reduced computational time.

Contribution

It demonstrates the effectiveness of non-local filters in spectrogram-based denoising and reveals a connection between Neighborhood filters and Nonlocal Means applied to the Wigner-Ville distribution.

Findings

Neighborhood filter reduces computational time significantly.

Non-local filters perform comparably to PDE-based filters.

The approach is validated on synthetic and biomedical signals.

Abstract

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.