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Image reconstruction in multi-channel model under Gaussian noise

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Abstract

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in a growing number, N, of independent channels in the Gaussian white noise. In each channel, the image and the background intensities are unknown. They define a set of unidentifiable nuisance parameters that slow down the typical minimax rate of convergence. The asymptotically minimax rate is found as N → ∞, and an asymptotically optimal estimator of the boundary function is suggested.

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Authors and Affiliations

  1. Wayne State University, Detroit, USA

    V. Holdai & A. Korostelev

Authors
  1. V. Holdai
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  2. A. Korostelev
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Correspondence to A. Korostelev.

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Holdai, V., Korostelev, A. Image reconstruction in multi-channel model under Gaussian noise. Math. Meth. Stat. 17, 198–208 (2008). https://doi.org/10.3103/S1066530708030022

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  • DOI: https://doi.org/10.3103/S1066530708030022

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