Anisotropic local approximations for pointwise adaptive signal-dependent noise removal

We present new methods for pointwise spatially-adaptive filtering of anisotropic multivariable signals. It is assumed that the observations are given by a broad class of models with a signal-dependent variance. The proposed methods are based on the local quasi-likelihood, incorporating the directional-windowed local polynomial approximations (LPA) of the signal. The intersection of confidence intervals (ICI) rule is used in order to determine the adaptive size of the directional windows. In this way we obtain multi-directional estimates which are spatially adaptive to unknown smoothness and anisotropy of the signal. Simulation experiments confirm the advanced performance of these new algorithms.