Directional varying scale approximations for anisotropic signal processing

A spatially adaptive restoration of a multivariable anisotropic function given by uniformly sampled noisy data is considered. The presentation is given in terms of image processing as it allows a convenient and transparent motivation of basic ideas as well as a good illustration of results. To deal with the anisotropy discrete directional kernel estimates equipped with varying scale parameters are exploited. The local polynomial approximation (LPA) technique is modified for a design of these kernels with a desirable polynomial smoothness. The nonlinearity of the method is incorporated by an intersection of confidence intervals (ICI ) rule exploited in order to obtain adaptive varying scales of the kernel estimates for each direction. In this way we obtain the pointwise varying scale algorithm which is spatially adaptive to unknown smoothness and anisotropy of the function in question. Simulation experiments confirm the advanced performance of the new algorithms.