Wavelet denoising based on local regularity information

We present a denoising method that is well fitted to the processing of extremely irregular signals such as (multi)fractal ones. Such signals are often encountered in practice, e.g., in biomedical applications. The basic idea is to estimate the regularity of the original data from the observed noisy ones using the large scale information, and then to extrapolate this information to the small scales. We present theoretical results describing the precise properties of the method. Numerical experiments show that this denoising scheme indeed performs well on irregular signals.