  An efficient algorithm for adaptive kernel smoothing (AKS) of two-dimensional
imaging data has been developed and implemented using the Interactive Data
Language (IDL). The functional form of the kernel can be varied (top-hat,
Gaussian etc.) to allow different weighting of the event counts registered
within the smoothing region. For each individual pixel the algorithm increases
the smoothing scale until the signal-to-noise ratio (s.n.r.) within the kernel
reaches a preset value. Thus, noise is suppressed very efficiently, while at
the same time real structure, i.e. signal that is locally significant at the
selected s.n.r. level, is preserved on all scales. In particular, extended
features in noise-dominated regions are visually enhanced. The ASMOOTH
algorithm differs from other AKS routines in that it allows a quantitative
assessment of the goodness of the local signal estimation by producing
adaptively smoothed images in which all pixel values share the same
signal-to-noise ratio above the background.
  We apply ASMOOTH to both real observational data (an X-ray image of clusters
of galaxies obtained with the Chandra X-ray Observatory) and to a simulated
data set. We find the ASMOOTHed images to be fair representations of the input
data in the sense that the residuals are consistent with pure noise, i.e. they
possess Poissonian variance and a near-Gaussian distribution around a mean of
zero, and are spatially uncorrelated.
