A METHOD BASED ON WAVELET TRANSFORMS FOR SOURCE DETECTION IN PHOTON-COUNTING DETECTOR IMAGES .1. THEORY AND GENERAL-PROPERTIES

We have developed a method based on wavelet transforms (WTs) to detect sources in astronomical images obtained with photon-counting detector s, such as X-ray images. The WT is a multiscale transform that is suit able for detection and analysis of interesting image features (sources ) spanning a range of sizes. This property of the WT is particularly w ell suited to the case in which the point-spread function is strongly varying across the image, and it is also effective in the detection of extended sources. The method allows one to measure source count rates , sizes, and ellipticity, with their errors. Care has been taken in th e assessment of thresholds for detection, in the WT space, at any desi red confidence level, through a detailed semianalytical study of the s tatistical properties of noise in wavelet-transformed images. The meth od includes the use of exposure maps to handle sharp background gradie nts produced by a nonuniform exposure across the detector, which would otherwise yield many spurious detections. The same method is applied to evaluate upper limits to the count rate of undetected objects in th e field of view, allowing a sensitivity map for each observation to be constructed.