## 213 Citations

A Parameter Selection Method for Wavelet Shrinkage Denoising

- Mathematics
- 2003

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

- Mathematics
- 2001

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

- Mathematics
- 2001

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.

- Computer ScienceMedical physics
- 1999

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

- Computer ScienceMedical Imaging
- 1997

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

- Computer Science, EngineeringIEEE Trans. Image Process.
- 2000

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

- MathematicsStat. Comput.
- 2002

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

- MathematicsIEEE Transactions on Image Processing
- 2006

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

- Mathematics
- 1999

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

- Computer Science
- 2007

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.

## References

SHOWING 1-10 OF 35 REFERENCES

Wavelet regression by cross-validation,

- Computer Science
- 1994

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

- Mathematics
- 1995

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?

- Computer Science
- 1995

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

- Mathematics
- 1975

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

- Mathematics
- 1978

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

- Mathematics
- 1994

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

- Computer ScienceIEEE 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

- MathematicsIEEE Trans. Inf. Theory
- 1992

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

- Computer Science
- 1992

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

- Mathematics
- 1985

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…