Hilbert vs. exponential Kernel functionals for Nonlocal Means image filtering

The present work introduces a new alternative to change the classical exponential kernel function used in Nonlocal Means (NLM) methods to deal with digital image filtering. The idea is based on the premise that making a good selection or estimation of the bandwidth parameter h is difficult and there are some other kernels which have another equivalent parameters to be selected into a more easiest way. A First method is obtained, when using an optimal manner proposed in nonparametric estimation literature to estimate h to tune the exponential kernel function. And a second proposed method, is to change the exponential function by the so called Hilbert function where one must to choose a parameter d. This Hilbert function is used for the first time in the NLM framework. Finally, the obtained filtering results reveals, that the NLM Hilbert kernel approach gives similar performance to other approaches according to recent reported results in literature, and the first proposed methodology is restricted by the estimation of h.