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

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Signal denoising methods based on the threshold processing of wavelet coefficients are widely used in various application areas. When applying these methods, it is usually assumed that the number of wavelet coefficients is fixed, and the noise distribution is Gaussian. Such a model has been well studied in the literature, and optimal threshold values have been calculated for different signal classes and loss functions. However, in some situations the sample size is not known in advance and is modeled by a random variable. In this paper, we consider a model with a random number of observations contaminated by a Gaussian noise, and study the behavior of the loss function based on the probabilities of errors in calculating wavelet coefficients for a growing sample size.

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Authors and Affiliations

  1. Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, Moscow, Russia

    O. V. Shestakov

  2. Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia

    O. V. Shestakov

Authors
  1. O. V. Shestakov
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Correspondence to O. V. Shestakov.

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Proceedings of the XXXIV International Seminar on Stability Problems for Stochastic Models, Debrecen, Hungary.

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Shestakov, O.V. Averaged Probability of the Error in Calculating Wavelet Coefficients for the Random Sample Size. J Math Sci 237, 826–830 (2019). https://doi.org/10.1007/s10958-019-04209-w

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  • DOI: https://doi.org/10.1007/s10958-019-04209-w

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