Wavelet shrinkage: unification of basic thresholding functions and thresholds

Wavelet shrinkage: unification of basic thresholding functions and thresholds

This work addresses the unification of some basic functions and thresholds used in nonparametric estimation of signals by shrinkage in the wavelet domain. The Soft and Hard thresholding functions are presented as degenerate smooth sigmoid based shrinkage functions. The shrinkage achieved by this new family of sigmoid based functions is then shown to be equivalent to a regularisation of wavelet ...

Choice of Thresholds for Wavelet Shrinkage Estimate of the Spectrum

We study the problem of estimating the log spectrum of a stationary Gaussian time series by thresholding the empirical wavelet coe cients. We propose the use of thresholds t j;n depending on sample size n, wavelet basis and resolution level j. At ne resolution levels (j= 1; 2; :::), we propose

Robust wavelet shrinkage using robust selection of thresholds

Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency

Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. In this paper, we will only consider the dependencies between the coefficients and their parents in detail. For this purpose, new non-Gaussian bivariate distributions are proposed, and correspond...

Adaptive Thresholding of Wavelet

Wavelet techniques have become an attractive and eecient tool in function estimation. Given noisy data, its discrete wavelet transform is an estimator of the wavelet coeecients. It has been shown by Donoho and Johnstone (1994) that thresholding the estimated coeecients and then reconstructing an estimated function reduces the expected risk close to the possible minimum. They ooered a global thr...