ASMOOTH: A simple and efficient algorithm for adaptive kernel smoothing of two-dimensional imaging data

Abstract

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.