A local geostatistical filtering method, called Local Kriging Analysis (L.K.A.), is presented in this paper. The method can be applied to image filtering, image enhancement and image restoration. This approach takes into consideration the spatial correlation of image intensities using the locally stationary auto-covariance function and is different in that sense from most filters classically used for image filtering. As the values of pixels which are close together are in general statistically correlated, geostatistics can be used to describe this spatial structure. In fact, the structural analysis of images often shows different correlation models at different scales (composite or nested models). This phenomenon of multiscaling dependence of pixel data can be used to separate several component images from the initial image by means of the kriging analysis technique. At this point, the method is equivalent to the spectral analysis for a stationary image, but can be extended to the non-stationary case using the intrinsic random function theory. In addition an adaptive moving correlation neighborhood can be chosen to locally estimate the different components.