Endoscopic imaging is a very important tool in modern medicine. Physicians set very high demands for image quality, but that quality is limited by endoscope fiber technology. This research addresses the problem of resolution enhancement of endoscopic images. A mathematical model of an endoscope was developed, describing an endoscope system as a Linear Space Invariant (LSI) filtering with sampling. The problem of image resolution improvement was considered as a Super Resolution (SR) problem. An efficient algorithm for calculating reconstruction discrete filters is presented, handling a general sampling grid. The problem of Moiré artifacts which is typical for images of fiber-scopes is discussed in this work. The processes involved in the creation of the artifacts are studied and modeled by the computer simulations. We explain how the technological breakthrough of the recent years in development of high-resolution imaging sensors can help to eliminate the problem of the artifacts.