Spatially adaptive estimation via fitted local likelihood (FLL) techniques

This paper offers a new technique for spatially adaptive estimation. The local likelihood is exploited for nonparametric modeling 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 are used for selection of an adaptive size and shape of this neighborhood. The algorithm is developed for a quite general class of observations subject to the exponential distribution. The estimated signal can be uniand multivariable. We demonstrate a good performance of the new algorithm for image denoising and compare the new method versus the intersection of confidence interval (ICI) technique that also exploits a selection of an adaptive neighborhood for estimation. Index Terms Adaptive nonparametric regression, adaptive non-Gaussian image denoising, anisotropic imaging, fitted local likelihood, non-Gaussian denoising, Poissonian denoising, varying threshold parameters EDICS: SSP-NPAR, SSP-FILT, ASP-ANAL