Abstract: This paper deals with the problem of function estimation. Using the white noise model setting, we provide a method to construct a new wavelet procedure based on thresholding rules which takes advantage of the dyadic structure of the wavelet decomposition. We prove that this new procedure performs very well since, on the one hand, it is adaptive and near-minimax over a large class of B...

De-noising algorithms based on wavelet thresholding replace small wavelet coeecients by zero and keep or shrink the coeecients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use Generalized Cross Validation. This procedure does not require an estimate for the noise en...

Wavelet based image denoising methods have attracted extensive interests over the last decade. Donoho et. al. [3] first suggested to remove/suppress noise by thresholding of wavelet coefficients. The underlying assumption is simple and intuitive: a wavelet coefficient is treated as noise and set to zero if it is below a preset threshold. Otherwise, the coefficient is kept or slightly modified. ...

This paper presents a novel wavelet-based denoising method using coefficient thresholding technique. The proposed method uses the adaptive thresholding which overcome the shortcomings of discontinuous function in hard-thresholding and also can eliminate the permanent bias in soft-thresholding. The qualitative evaluation of the denoising performance has shown that the proposed method cancels noi...

In this paper, we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced. The approach can apply readily to many other statistical contexts. Various new penalty functions are proposed. The hard-thresholding and soft-thresholding estimators of Donoho and Johnstone are speciŽ c members of nonlinear regular...

Wavelet based image denoising methods have attracted extensive interests over the last decade. Donoho et. al. [3] first suggested to remove/suppress noise by thresholding of wavelet coefficients. The underlying assumption is simple and intuitive: a wavelet coefficient is treated as noise and set to zero if it is below a preset threshold. Otherwise, the coefficient is kept or slightly modified. ...

Approaches to wavelet-based denoising (or signal enhancement) have generally relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on the minimax description length (MMDL) principle. We first determine the least favorable distribution in the "-contaminated normal fami...

To analyze EEG accurately, it is necessary to remove artifacts from EEG, which gets coupled with signal at the time of recording and can’t be eliminated at preprocessing stage. Ocular artifact is most obvious artifact in EEG. In this paper, a new method using Stationary Wavelet Enhanced Independent Component Analysis with a novel thresholding, is proposed for ocular artifact removal from EEG. P...