In the nanometer resolution range, image formation in scanning tunneling microscopy and atomic force microscopy is essentially governed by the geometrical interaction between the specimen surface and the tip surface. This nonlinear process can be described by using the tools of mathematical morphology. In principle, if the tip shape is precisely known, an image restoration can be performed. In this article, the capabilities of a blind restoration procedure which needs neither a precise knowledge of the tip shape nor the use of a known test object are presented. The efficiency of the blind restoration is demonstrated on an experimental atomic force microscopy image of a DNA molecule obtained in the "tapping mode".