A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior; and iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `hundreds' as compared to existing Bayesian source extraction methods that use MCMC to explore the parameter space, such as that presented by Hobson & McLachlan. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (Version-I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted for publication in MNRA

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

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.Comment: 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 submissio

Near-infrared reddening of extra-galactic GMCs in a face-on geometry

[Abridged] We describe the near-infrared reddening signature of giant molecular clouds (GMCs) in external galaxies. In particular, we examine the E(J-H) and E(H-K) color-excesses, and the effective extinction law observed in discrete GMC regions. We also study the effect of the relative scale height of the GMC distribution to the color-excesses, and to the observed mass function of GMCs. We perform Monte Carlo radiative transfer simulations with 3D models of stellar radiation and clumpy dust distributions, resembling a face-on geometry. The scattered light is included in the models, and near-infrared color maps are calculated from the simulated data. The effective near-infrared reddening law, i.e. the ratio E(J-H)/E(H-K), has a value close to unity in GMC regions. The ratio depends on the relative scale height of GMCs, xi, and for xi values 0.1...0.75 we find the typical ratios of 0.6...1.1. The effective extinction law turns out to be very flat in GMC regions. We find the ratios of apparent extinctions of A(H)/A(K)=1.35...1.55 and A(J)/A(H)=1.15. The effect of the scattered flux on the effective reddening law, as well as on the effective extinction law, is significant. Regarding the GMC mass function, we find no correlation between the input and observed slopes of the mass functions. Rather, the observed slope reflects the parameter $\xi$ and the dynamical range of the mass function. We estimate that only a fraction of 10...20 % of the total mass of GMCs is recovered, if the observed color-excess values are transformed to masses using the Galactic reddening law. In the case of individual clouds the fraction can vary between ~0...50 %.Comment: 8 pages, 10 figures, accepted for publication in A&A. Added missing histograms in Fig.

Substructures in WINGS clusters

We search for and characterize substructures in the projected distribution of galaxies observed in the wide field CCD images of the 77 nearby clusters of the WIde-field Nearby Galaxy-cluster Survey (WINGS). This sample is complete in X-ray flux in the redshift range 0.04<z<0.07. We search for substructures in WINGS clusters with DEDICA, an adaptive-kernel procedure. We test the procedure on Monte-Carlo simulations of the observed frames and determine the reliability for the detected structures. DEDICA identifies at least one reliable structure in the field of 55 clusters. 40 of these clusters have a total of 69 substructures at the same redshift of the cluster (redshift estimates of substructures are from color-magnitude diagrams). The fraction of clusters with subclusters (73%) is higher than in most studies. The presence of subclusters affects the relative luminosities of the brightest cluster galaxies (BCGs). Down to L ~ 10^11.2 L_Sun, our observed differential distribution of subcluster luminosities is consistent with the theoretical prediction of the differential mass function of substructures in cosmological simulations.Comment: A&A accepted - figure 6 is available from http://adlibitum.oats.inaf.it/ramella/WINGSfig

Calculation of the detection properties in the binary symmetrical channel

summary:One of the important parts of railway signalling systems design is the safety of communication, achievable - among others - with the error detecting code. Getting evidence of quantitative safety targets, especially the probability of undetected error of the code, is a surprisingly complicated issue. We've analysed 2048 irreducible self-adjoint generator polynomials of the degree 32. More than 70 of these have a maximum probability of failure lower than the standard codes generally used. In this article we present the best of all codes we've analysed