Nonlinear wavelet thresholding: A recursive method to determine the optimal denoising threshold

Nonlinear thresholding of wavelet coefficients is an efficient method for denoising signals with isolated singularities. The quasi-optimal value of the threshold depends on the sample size and on the variance of the noise, which is in many situations unknown. We present a recursive algorithm to esti...

Full description

Saved in:
Bibliographic Details
Published inApplied and computational harmonic analysis Vol. 18; no. 2; pp. 177 - 185
Main Authors Azzalini, Alexandre, Farge, Marie, Schneider, Kai
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2005
Subjects
Data analysis
Denoising
Estimation
Wavelets
Wavelets
Data analysis
Estimation
Denoising
Online AccessGet full text

Cover

More Information
Summary:Nonlinear thresholding of wavelet coefficients is an efficient method for denoising signals with isolated singularities. The quasi-optimal value of the threshold depends on the sample size and on the variance of the noise, which is in many situations unknown. We present a recursive algorithm to estimate the variance of the noise, prove its convergence and investigate its mathematical properties. We show that the limit threshold depends on the probability density function (PDF) of the noisy signal and that it is equal to the theoretical threshold provided that the wavelet representation of the signal is sufficiently sparse. Numerical tests confirm these results and show the competitiveness of the algorithm compared to the median absolute deviation method (MAD) in terms of computational cost for strongly noised signals.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2004.10.001