Restoration of scanning-tunneling-microscope data blurred by limited resolution, and hampered by 1 f-like noise

Least-squares or Wiener filters are powerful tools to restore blurred and noisy pictures. For an optimal implementation, a knowledge of the noise and of the point-spread function (PSF) is needed; whereas the resolution PSF is relatively well known from recent theories of STM, the noise spectrum can be investigated by recording and analyzing the signal of the feedback which should keep the tunneling current constant. A 1 fβ noise spectrum is found with β = 1.4 ± 0.2. This noise can give rise to pretended hills and valleys or to spurious stripes parallel to the scanning direction in STM images. With a Wiener filter, in which the model noise-to-signal ratio is 1 fβ-like, these artificial features are eliminated. However, since the noise spectrum may partly overlap the desired spectrum of the surface corrugation, care has to be taken not to generate new artifacts. © 1987.