Spatially adaptive estimation via fitted local likelihood techniques
- Katkovnik, Vladimir
- Spokoiny, Vladimir
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.
- IEEE Trans. Signal Process., 56 (2008) pp. 873--886.