Rearranged nonlocal filters for signal denoising

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 non-local filters, like Neighborhood or Yaroslavsky filters, in the same problem. The reformulation of the Neighborhood filter using the decreasing rearrangement allows us to implement an efficient algorithm. The integral histogram introduced by Porikli allows him in Porikli (2008) to obtain an implementation of the Yaroslavsky filter with a computational cost independent of the size of the box spatial local kernel. We heuristically justify 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.