A Wavelet-based algorithm for the spatial analysis of Poisson data

Aug, 2001
34 pages
Published in:
  • Astrophys.J.Suppl. 138 (2002) 185-218
e-Print:

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Abstract: (arXiv)
Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly non-zero correlation coefficients will be observed only where there are high-order variations in the data: e.g., they will be observed in the vicinity of sources. In this paper, we describe the mission-independent, wavelet-based source detection algorithm WAVDETECT, part of the CIAO software package. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e. flat-fielded) background maps: (2) the correction for exposure variations within the field-of-view: (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds: (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape: and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the algorithm's robustness by applying it to various images.
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