Generalized cross validation for wavelet thresholding

  title={Generalized cross validation for wavelet thresholding},
  author={Maarten Jansen and Maurits Malfait and Adhemar Bultheel},
  journal={Signal Process.},

Figures from this paper

A Parameter Selection Method for Wavelet Shrinkage Denoising
Thresholding estimators in an orthonormal wavelet basis are well established tools for Gaussian noise removal. However, the universal threshold choice, suggested by Donoho and Johnstone, sometimes
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study
This paper discusses in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provides an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data.
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
Image de-noising by integer wavelet transforms and generalized cross validation.
This paper uses the method for wavelet transforms that map integer gray-scale pixel values to integer wavelet coefficients to estimate the optimal threshold, which minimizes the error of the result as compared to the unknown, exact data.
Wavelet-based image denoising using generalized cross validation
This paper uses generalized cross validation to estimate the optimal threshold for de-noising algorithms, which assumes uncorrelated noise, and an orthogonal wavelet transform.
Adaptive wavelet thresholding for image denoising and compression
An adaptive, data-driven threshold for image denoising via wavelet soft-thresholding derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution widely used in image processing applications.
Choice of wavelet smoothness, primary resolution and threshold in wavelet shrinkage
A fast cross-validation algorithm that performs wavelet shrinkage on data sets of arbitrary size and irregular design and also simultaneously selects good values of the primary resolution and number of vanishing moments is introduced.
A semi-local paradigm for wavelet denoising
Experiments with phantom PET images show that the semi-local paradigm provides superior denoising compared to standard application of the GCV technique, and an asymptotic analysis demonstrates that, under some regularity conditions, semi- Local Denoising is asymPTotically consistent on the logarithmic scale.
Empirical Bayes Approach to Improve Wavelet Thresholding for Image Noise Reduction
This article introduces a geometrical prior model for configurations of important wavelet coefficients and combines this with local characterization of a classical threshold procedure into a Bayesian framework, which is incorporated into the conditional model.
Smoothing Non-equidistantly Sampled Data Using Wavelets and Cross Validation
This paper investigates how to apply algorithms developed for wavelet decompositions of non-equidistant samples, using so called second generation wavelets to reduce noise in signals on a non-Equidistant grid.


Wavelet regression by cross-validation,
The main aim of the paper is to introduce and develop a cross-validation method for selecting a wavelet regression threshold that produces good estimates with respect to L2 error and compare it with other threshold-choice methods for a three functions and three diierent noise structures.
Adapting to Unknown Smoothness via Wavelet Shrinkage
Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet
Wavelet Shrinkage: Asymptopia?
A method for curve estimation based on n noisy data: translate the empirical wavelet coefficients towards the origin by an amount √(2 log n) /√n and draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves.
Smoothing noisy data with spline functions
It is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m−1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed
Smoothing noisy data with spline functions
SummarySmoothing splines are well known to provide nice curves which smooth discrete, noisy data. We obtain a practical, effective method for estimating the optimum amount of smoothing from the data.
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,
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
  • S. Mallat
  • Computer Science
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 1989
It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Singularity detection and processing with wavelets
It is proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents.
On the feasibility of cross-validation in image analysis
It is shown that cross-validation results in asymptotically optimal performance, provided the amount of blur does not exceed a certain ceiling, and the ceiling is surprisingly low.
Smoothing noisy data with spline functions
SummaryA procedure for calculating the trace of the influence matrix associated with a polynomial smoothing spline of degree2m−1 fitted ton distinct, not necessarily equally spaced or uniformly