A WaveletBased Algorithm for the Spatial Analysis of Poisson Data
Abstract
Wavelets are scalable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero, and thus may be used to simultaneously characterize the shape, location, and strength of astronomical sources. But in addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Waveletbased source detection involves the correlation of scaled wavelet functions with binned, twodimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly nonzero correlation coefficients will be observed only where there are highorder variations in the data; e.g., they will be observed in the vicinity of sources. Source pixels are identified by comparing each correlation coefficient with its probability sampling distribution, which is a function of the (estimated or a priori known) background amplitude. In this paper, we describe the missionindependent, waveletbased source detection algorithm ``WAVDETECT,'' part of the freely available Chandra Interactive Analysis of Observations (CIAO) software package. Our algorithm uses the Marr, or ``Mexican Hat'' wavelet function, but may be adapted for use with other wavelet functions. Aspects of our algorithm include: (1) the computation of local, exposurecorrected normalized (i.e., flatfielded) background maps; (2) the correction for exposure variations within the field of view (due to, e.g., telescope support ribs or the edge of the field); (3) its applicability within the lowcounts 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 Xray image data, especially in the low count regime. We demonstrate the robustness of WAVDETECT by applying it to an image from an idealized detector with a spatially invariant Gaussian PSF and an exposure map similar to that of the Einstein IPC; to Pleiades Cluster data collected by the ROSAT PSPC; and to simulated Chandra ACISI image of the Lockman Hole region.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 January 2002
 DOI:
 10.1086/324017
 arXiv:
 arXiv:astroph/0108429
 Bibcode:
 2002ApJS..138..185F
 Keywords:

 Methods: Data Analysis;
 Techniques: Image Processing;
 XRays: General;
 Astrophysics
 EPrint:
 Accepted for publication in Ap. J. Supp. (v. 138 Jan. 2002). 61 pages, 23 figures, expands to 3.8 Mb. Abstract abridged for astroph submission