XMM-Newton Science Analysis System


ewavelet (ewavelet-3.11.2) [xmmsas_20160201_1833-15.0.0]

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Background estimation

The wavelet detection algorithm itself does not use any separate background estimate. However, for determining the significance of a candidate source detection the background value at a given pixel coordinate has to be known.

At the moment the background is calculated by smearing the image with a function of the form

$r^2/\sigma^2\exp(-0.5r^2/\sigma^2)$ .

This function is related to the Mexican hat function through its Fourier Transform. It has the nice property that it weighs more the outside ring, so that possible sources do not give too much of a strong signal at the source position. For the $\sigma$ parameter I choose to use a value twice the size of the wavelet scale under investigation (so for every scale a different background map is generated).

After one iteration the input for the background estimate is the original image minus the sources, detected at scales smaller or equal to the wavelet scale under investigation. In this way sources with a large extent are modelled in the background map. This prevents spurious detections of small sources within the envelope of extended sources.