Statistical Properties of Wavelet Transforms Applied to X-Ray Source Detection

Abstract

We have developed a method for detection of sources in X-ray images, based on wavelet transforms (WT). After having computed the WT of an image, for various values of the wavelet scale parameter, candidate sources are selected as local maxima in the wavelet-transformed image. The reliable discrimination between true sources and random background fluctuations requires a detailed knowledge of the distribution of WT values arising only from background noise. The shape of this distribution may be very different from a Gaussian, especially in the limit of few counts per image resolution element, which is the case in most X-ray images. By means of both analytical means and numerical simulations, we have therefore studied the WT probability distribution for a wide range of background density values. This enables us to derive thresholds for source detection in the WT images, for a range of confidence levels. These detection thresholds are now being used in our detection algorithm with good results.