Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise
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 ta...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/377 |
| _version_ | 1818483697270128640 |
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| author | Oleg Shestakov |
| author_facet | Oleg Shestakov |
| author_sort | Oleg Shestakov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T15:45:21Z |
| format | Article |
| id | doaj.art-ef8d19bbe323474c9c9ee2c02f418982 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-10T15:45:21Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ef8d19bbe323474c9c9ee2c02f4189822022-12-22T01:42:58ZengMDPI AGMathematics2227-73902020-03-018337710.3390/math8030377math8030377Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated NoiseOleg Shestakov0Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, Moscow 119991, RussiaSignal 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.https://www.mdpi.com/2227-7390/8/3/377threshold processingrandom sampleslong-term dependencemean-square risk estimate |
| spellingShingle | Oleg Shestakov Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise Mathematics threshold processing random samples long-term dependence mean-square risk estimate |
| title | Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise |
| title_full | Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise |
| title_fullStr | Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise |
| title_full_unstemmed | Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise |
| title_short | Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise |
| title_sort | wavelet thresholding risk estimate for the model with random samples and correlated noise |
| topic | threshold processing random samples long-term dependence mean-square risk estimate |
| url | https://www.mdpi.com/2227-7390/8/3/377 |
| work_keys_str_mv | AT olegshestakov waveletthresholdingriskestimateforthemodelwithrandomsamplesandcorrelatednoise |