Asymptotically optimal wavelet thresholding in models with non-Gaussian noise distributions

Kudryavtsev, A. A.; Shestakov, O. V.

doi:10.1134/s1064562416060028

Cited by 7 publications

(1 citation statement)

References 7 publications

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“…This transform is applied to data, and the threshold processing of the resulting wavelet coefficients is performed [1]. For a model of signal samples with an equispaced grid, these methods were well studied by D. Donoho, I. Johnstone, B. Silverman and others [2][3][4][5][6][7][8][9][10]. Statistical properties of the mean-square risk estimator were also studied.…”

Section: Introductionmentioning

confidence: 99%

Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise

Shestakov

2020

Mathematics

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Signal de-noising methods based on threshold processing of wavelet decomposition coefficients have become popular due to their simplicity, speed, and ability to adapt to signal functions with spatially inhomogeneous smoothness. The analysis of the errors of these methods is an important practical task, since it makes it possible to evaluate the quality of both methods and equipment used for processing. Sometimes the nature of the signal is such that its samples are recorded at random times. If the sample points form a variational series based on a sample from the uniform distribution on the data registration interval, then the use of the standard threshold processing procedure is adequate. The paper considers a model of a signal that is registered at random times and contains noise with long-term dependence. The asymptotic normality and strong consistency properties of the mean-square thresholding risk estimator are proved. The obtained results make it possible to construct asymptotic confidence intervals for threshold processing errors using only the observed data.

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Section: Introductionmentioning

confidence: 99%

Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise

Shestakov

2020

Mathematics

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Estimation of the Loss Function When Using Wavelet-Vaguelette Decomposition for Solving Ill-Posed Problems

Kudryavtsev

Shestakov

2019

J Math Sci

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Averaged Probability of the Error in Calculating Wavelet Coefficients for the Random Sample Size

Shestakov

2019

J Math Sci

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Asymptotically optimal wavelet thresholding in models with non-Gaussian noise distributions

Cited by 7 publications

References 7 publications

Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise

Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise

Estimation of the Loss Function When Using Wavelet-Vaguelette Decomposition for Solving Ill-Posed Problems

Averaged Probability of the Error in Calculating Wavelet Coefficients for the Random Sample Size

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