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A Wavelet‐Based Algorithm for the Spatial Analysis of Poisson Data

2001/08/27 by P. E. Freeman, Peter E. Freeman, Vinay Kashyap +5 · 594 citations
Computer Science · Medicine · Physics and Astronomy · #Computation #Function (biology) #Image (mathematics) #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Pixel #Poisson distribution #Radiation Detection and Scintillator Technologies #Robustness (evolution) #Wavelet #Wavelet transform #astro-ph

paper · pdf · doi:10.1086/324017

published in The Astrophysical Journal Supplement Series 138(1), 185-218 (Institute of Physics) · Accepted for publication in Ap. J. Supp. (v. 138 Jan. 2002). 61 pages, 23 figures, expands to 3.8 Mb. Abstract abridged for astro-ph submission

arxiv created 2001/08/27 · openalex publication_date 2002/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

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. 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 nonzero 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. 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 mission-independent, wavelet-based 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, exposure-corrected normalized (i.e., flat-fielded) 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 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 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 ACIS-I image of the Lockman Hole region.

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