Abstract
Title : Artifact Free Signal Denoising With Wavelets
Authors : Sylvain Durand and Jacques Froment
Recent years have seen the development of signal denoising algorithms
based on wavelet transform. It has been shown that thresholding
the wavelet coefficients of a noisy signal allows to restore the
smoothness of the original signal.
This approach is shared by all
decompositions in orthogonal bases, but the wavelet one is particularly
adapted since piecewise smooth signals lead sorted wavelet coefficients
with fast decay.
However, wavelet denoising suffers of a main drawback :
around discontinuities the reconstructed signal is smoothed, exhibiting
pseudo-Gibbs phenomenon. We consider the problem of
denoising piecewise smooth signals with sharp discontinuities. We
propose to apply a traditional wavelet denoising method and to restore the
denoised signal using a total variation minimization approach. This second
step allows to remove the Gibbs phenomena and therefore to restore sharp
discontinuities, while the other structures are preserved.
The main innovation of our algorithm is to constrain the total variation
minimization by the knowledge of the remaining wavelet coefficients.
In this way, we make sure that the restoration process
does not deteriorate the information that has been considered as significant
in the denoising step. With this approach we substantially improve
the performance of classical wavelet denoising algorithms, both in terms
of SNR and in terms of visual artifacts.