WIAS Preprint No. 1166, (2006)

Spatially adaptive estimation via fitted local likelihood techniques


  • Katkovnik, Vladimir
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62G20


  • local model selection, fitted likelihood, adaptive estimation




This paper offers a new technique for spatially adaptive estimation. The local likelihood is exploited for nonparametric modelling of observations and estimated signals. The approach is based on the assumption of a local homogeneity of the signal: for every point there exists a neighborhood in which the signal can be well approximated by a constant. The fitted local likelihood statistics is used for selection of an adaptive size of this neighborhood. The algorithm is developed for quite a general class of observations subject to the exponential distribution. The estimated signal can be uni- and multivariable. We demonstrate a good performance of the new algorithm for Poissonian image denoising and compare of the new method versus the intersection of confidence interval $(ICI) $ technique that also exploits a selection of an adaptive neighborhood for estimation.

Appeared in

  • IEEE Trans. Signal Process., 56 (2008) pp. 873--886.

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