NONLINEAR DIGITAL FILTERING OF SCANNING-PROBE-MICROSCOPY IMAGES BY MORPHOLOGICAL PSEUDOCONVOLUTIONS

A recently developed class of digital filters known as morphological pseudoconvolutions is applied to scanning tunneling microscopy (STM) images. These filters use a nonlinear branch of image processing known as morphology to improve the characteristics of both moving mean and moving median filters. They filter equally in both the x and y directions, so as not to introduce artifacts, and they have an adjustable parameter that allows the user to restore the observed image completely as the parameter tends to infinity. Very few assumptions are made concerning image and noise content; only the shape of typical data is taken into account. These filters are shown to outperform, both visually and in the mean-square-error sense, previously introduced Wiener filtering techniques. The filters are compared on typical STM-type images, using both modeled and actual data. The technique is general, and has been shown to perform very well on all types of STM and atomic force microscopy images.