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Wavelets and Estimation of Discontinuous Functions

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Abstract

The paper considers the problem of estimating a signal with finitely many points of discontinuity from observations against white Gaussian noise. It is shown that, with an appropriate choice of a generator polynomial, an estimation method based on wavelets yields asymptotically minimax (up to a constant) estimates for functions sufficiently smooth outside the discontinuity points.

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Authors and Affiliations

  1. Institute for Information Transmission Problems, RAS, Moscow

    L. L. Boiko

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  1. L. L. Boiko
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Boiko, L.L. Wavelets and Estimation of Discontinuous Functions. Problems of Information Transmission 40, 226–236 (2004). https://doi.org/10.1023/B:PRIT.0000044258.38384.99

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  • DOI: https://doi.org/10.1023/B:PRIT.0000044258.38384.99

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