KEYWORDS: Sensors, Optical filters, Modulation transfer functions, Linear filtering, Image filtering, Signal detection, Optimal filtering, Numerical simulations, Digital filtering, Astronomy
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.
We present scale-adaptive filters that optimize the detection/separation of compact sources on a background. We assume that the sources have a multiquadric profile and a background modeled by an homogeneous and isotropic random field characterized by a power spectrum. We make an n-dimensional treatment but consider two interesting physical applications related to clusters of galaxies (Sunyaev-Zel'dovich effect and X-ray emission). We extend this methodology to multifrequency maps, introducing multifilters that optimize the detection on clusters on microwave maps. We apply these multifilters to small patches (corresponding to 10 frequency channels) of the sky such as the ones that will produce the future ESA Planck mission. Our method predicts a number of ≈10000 clusters in 2/3 of the sky, being the catalog complete over fluxes S > 170mJy at 300GHz.
We present a method to detect non-Gaussianity in CMB temperature fluctuations maps, based on the spherical Mexican Hat wavelet. We have applied this method to artificially generated non-Gaussian maps using the Edgeworth expansion. Analysing the skewness and kurtosis of the wavelet coefficients in contrast to Gaussian simulations, the Mexican Hat is more efficient in detecting non-Gaussianity than the spherical Haar wavelet for all different leves of non-Gaussianity introduced. These results are relevant to test the Gaussian character of the CMB data. The method has also been applied to non-Gaussian maps generated by introducing an additional quadratic term in the gravitational potential.
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