Local Regularity Preserving Signal Denoising I: Holder Exponents
Antoine Echelard, Lévy Véhel, Jacques · HAL (Le Centre pour la Communication Scientifique Directe) · 2013
We propose a denoising method that has the property of preserving local regularity, in the sense of local Hölder exponent. This approach is fitted to the processing of irregular signals, and gives specially relevant results for those displaying a local form of scale invariance known as localisability. A wavelet decomposition is used to measure and control the local Hölder exponent. The main ingredient of the algorithm is an estimator (which is of independent interest) of the time-dependent cut-off scale beyond which wavelet coefficients are mainly due to noise. Based on local regularity estimated from information below the cut-off scale, these small-scale coefficients-which govern the texture- are cor-rected so that the Hölder exponent of the denoised signal matches the one of the original signal. The processing is only slightly more com-plex than classical wavelet coefficients thresholding, resulting in fast computing times. Numerical experiments show the good performance of this scheme on various localisable signals. 1 Recalls on Hölder exponents and notations We use the following notation throughout: f is a continuous-time signal that is always assumed to belong to the global Hölder space C((0, 1)) for some