A Bayesian approach to filter design: detection of compact sources

Abstract

We consider filters for the detection and extraction of compact sources on a background. We make a one-dimensional treatment (though a generalization to two or more dimensions is possible) assuming that the sources have a Gaussian profile whereas the background is modeled by an homogeneous and isotropic Gaussian random field, characterized by a scale-free power spectrum. Local peak detection is used after filtering. Then, a Bayesian Generalized Neyman-Pearson test is used to define the region of acceptance that includes not only the amplification but also the curvature of the sources and the a priori probability distribution function of the sources. We search for an optimal filter between a family of Matched-type filters (MTF) modifying the filtering scale such that it gives the maximum number of real detections once fixed the number density of spurious sources. We have performed numerical simulations to test theoretical ideas.

10 pages, 2 figures. SPIE Proceedings "Electronic Imaging II", San Jose, CA. January 2004

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Cited by in corpus (8)

• Non-blind catalogue of extragalactic point sources from the Wilkinson Microwave Anisotropy Probe (WMAP) first 3--year survey data
• Matrix Filters for the Detection of Extragalactic Point Sources in Cosmic Microwave Background Images
• A novel multi-frequency technique for the detection of point sources in Cosmic Microwave Background maps
• Filter design for the detection of compact sources based on the Neyman-Pearson detector
• A multifrequency method based on the Matched Multifilter for the detection of point sources in CMB maps
• Effect of component separation on the temperature distribution of the CMB
• Detection of point sources on two-dimensional images based on peaks
• Multi-frequency point source detection with fully convolutional networks: Performance in realistic microwave sky simulations