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Stabilized Hard Thresholding of Wavelet-Vaguelette Decomposition Coefficients in Reconstructing Tomographic Images Using Projections with Correlated Noise

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Abstract

A way of reconstructing tomographic images based on wavelet-vaguelette decomposition is considered for a model with correlated additive noise. The asymptotic properties of an unbiased estimator are studied for the mean-square risk with stabilized hard thresholding of the coefficients of decomposition. It is shown that under certain conditions, this estimator is strongly consistent and asymptotically normal.

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Funding

This work was partially supported by the Russian Foundation for Basic Research, project no. 19-07-00352.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    O. V. Shestakov

  2. Institute of Informatics Problems, Federal Research Center Computer Science and Control, Russian Academy of Sciences, Moscow, 119333, Russia

    O. V. Shestakov

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

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Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2019, No. 3, pp. 53–57.

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Shestakov, O.V. Stabilized Hard Thresholding of Wavelet-Vaguelette Decomposition Coefficients in Reconstructing Tomographic Images Using Projections with Correlated Noise. MoscowUniv.Comput.Math.Cybern. 43, 133–137 (2019). https://doi.org/10.3103/S0278641919030063

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  • DOI: https://doi.org/10.3103/S0278641919030063

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