Restoration of Binary
نویسنده
چکیده
In this paper the problem of the restoration of binary images from Ber-noulli random noise is investigated. Assuming that an image has regular boundary, we show that linear averaging estimators are nearly optimal up to a logarithmic factor of the number of pixels. Moreover, we provide examples showing that for any estimator there exist images with regular boundary such that an estimation error is of the order of the size of this boundary. Furthermore we introduce a class of hierarchical threshold estimators which are wavelet based estimators achieving this lower bound. In terms of Besov norms these estimators have optimal convergence rates. Some simulation examples illustrate the performance of these estimators.
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