Smooth sigmoid wavelet shrinkage for non-parametric estimation

@article{Atto2008SmoothSW,
  title={Smooth sigmoid wavelet shrinkage for non-parametric estimation},
  author={Abdourrahmane Mahamane Atto and Dominique Pastor and Gr{\'e}goire Mercier},
  journal={2008 IEEE International Conference on Acoustics, Speech and Signal Processing},
  year={2008},
  pages={3265-3268}
}
  • A. AttoDominique PastorG. Mercier
  • Published 12 May 2008
  • Materials Science, Computer Science
  • 2008 IEEE International Conference on Acoustics, Speech and Signal Processing
This paper presents a new sigmoid-based wave shrink function. The shrinkage obtained via this function is particularly suitable to reduce noise without impacting significantly the statistical properties of the signal to be recovered. The proposed WaveShrink function depends on a parameter that makes it possible to control the attenuation degree imposed to the data, and thus, allows for a flexible shrinkage. 

Figures and Tables from this paper

Smooth Adaptation by Sigmoid Shrinkage

This paper provides a SURE optimization for the parameters of the SigShrink functions, which is performed on an unbiased estimation risk obtained by using the functions of this subclass of sigmoid-based shrinkage functions.

Wavelet shrinkage: unification of basic thresholding functions and thresholds

This work addresses the unification of some basic functions and thresholds used in non-parametric estimation of signals by shrinkage in the wavelet domain and shows that the non-degenerate sigmoid shrinkage adjusted with the new detection thresholds is as performant as the best up-to-date parametric and computationally expensive method.

Searching Appropriate Mother Wavelets for Hyperanalytic Denoising

A new variant of Hyperanalytic Wavelet Transform with a maximum a posteriori (MAP) filter, named bishrink for the denoising of images affected by additive white Gaussian noise (AWGN).

Wavelet Shrinkage: From Sparsity and Robust Testing to Smooth Adaptation

This chapter presents several theoretical results, from which new adaptable WaveShrink estimators are derived that overcome the limitations of standard ones, have an explicit close form and can apply to any wavelet transform and to a large class of estimation problems.

Block Smoothed Sigmoid-Based Shrinkage in Time-Frequency Domain for Robust Audio Denoising

A novel robust method for short-time spectral amplitude (STSA) estimation in audio denoising by extending the smoothed sigmoid-based shrinkage (SSBS), which does not require any prior information about the probability distribution of the signal of interest.

Sparsity Measure and the Detection of Significant Data

The paper provides a formal description of the sparsity of a representation via the detection thresholds, derived from theoretical results about the detection of significant coefficients when data are observed in presence of additive white Gaussian noise.

Joint Soft Threshold and Statistical Estimation for Speech Enhancement

A novel method for speech enhancement based on the combination of sigmoid shrinkage and bayesian estimator to apply a joint detection and estimation to noisy speech before using a standard minimum-mean-squared-error estimator.

Sparsity from binary hypothesis testing and application to non-parametric estimation

Prospects are suggested for estimating unknown signals in non-necessarily white or Gaussian noise in the context of non-parametric estimation by soft thresholding in the wavelet domain using level-dependent detection thresholds.

Sigmoid shrinkage for BM3D denoising algorithm

A modified version of the BM3D algorithm recently introduced by Dabov et al. is proposed for the denoising of images corrupted by additive white Gaussian noise, with an improvement on the thresholding of wavelet coefficients.

References

SHOWING 1-5 OF 5 REFERENCES

A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

An interscale orthonormal wavelet thresholding algorithm is described based on this new approach and its near-optimal performance is described by comparing it with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images.

Image denoising using scale mixtures of Gaussians in the wavelet domain

The performance of this method for removing noise from digital images substantially surpasses that of previously published methods, both visually and in terms of mean squared error.

Regularization of Wavelet Approximations

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

Ideal spatial adaptation by wavelet shrinkage

SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline,

Waveshrink shrinkage denoising using the nonnegative garrote

  • Journal of Computational and Graphical Statistics, vol. 7, no. 4, 1998.
  • 1998