Wavelet Based X-Ray Spatial Analysis: Statistical Issues

Abstract

We use a wavelet-based algorithm to detect and characterize sources in astronomical X-ray images, which consists of correlating binned data with the Mexican-Hat function (MexHat):

$$MH(x,y) = (2 - \frac{{{x^2}}}{{\sigma _x^2}} - \frac{{{y^2}}}{{\sigma _y^2}}){e^{ - \frac{{{x^2}}}{{2\sigma _x^2}} - \frac{{{y^2}}}{{2\sigma _y^2}}}}$$

Use of the algorithm over a grid of scales (σ _x ,σ _y ) in principle allows us to de tect and characterize sources.