# An α-stable approach to the study of the P(D) distribution of unresolved point sources in CMB sky maps

@article{Herranz2004AnA, title={An $\alpha$-stable approach to the study of the P(D) distribution of unresolved point sources in CMB sky maps}, author={Diego Herranz and Ercan Engin Kuruoglu and Luigi Toffolatti}, journal={Astronomy and Astrophysics}, year={2004}, volume={424}, pages={1081-1096} }

We present a new approach to the statistical study and modelling of number counts of faint point sources in astro- nomical images, i.e. counts of sources whose flux falls below the detection limit of a survey. The approach is based on the theory of α-stable distributions. We show that the non-Gaussian distribution of the intensity fluctuations produced by a generic point source population - whose number counts follow a simple power law - belongs to the α-stable family of distributions. Even if…

## 23 Citations

Confusion Noise due to Clustered Extragalactic Point Sources. Application of Logarithmic Cumulants for Parameter Estimation

- Physics, MathematicsPublications of the Astronomical Society of the Pacific
- 2019

The calculation of the characteristic function of the signal fluctuations due to clustered astrophysical sources is performed in this paper. For the typical case of power-law differential number…

Statistical analysis of undetected point sources in cosmic microwave background maps

- Physics
- 2006

Cosmic microwave background (CMB) temperature anisotropies follow a Gaussian statistical distribution in the standard inflationary model, but there are non-Gaussian contributions due to astrophysical…

Submillimeter number counts from statistical analysis of BLAST maps

- Physics
- 2009

We describe the application of a statistical method to estimate submillimeter galaxy number counts from confusion-limited observations by the Balloon-borne Large Aperture Submillimeter Telescope…

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- Physics
- 2004

We present predictions of the angular power spectrum of cosmic microwave background (CMB) fluctuations due to extragalactic point sources (EPSs) by using a method for simulating realistic…

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- Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2008

A fully Bayesian source separation technique that assumes a very flexible model for the sources, namely the Gaussian mixture model with an unknown number of factors, and utilize Markov chain Monte Carlo techniques for model parameter estimation is developed.

Anomalous diffusion of cosmic rays: A geometric approach

- Physics
- 2021

In this work, we analyze the process leading to the occurrence of anomalous transport phenomena associated with galactic cosmic rays propagating through the interstellar space. The origin of…

Fully Bayesian Blind Source Separation of Astrophysical Images Modelled by Mixture of Gaussians

- 2008

In this work, we address the problem of source separation in the presence of prior information. We develop a fully Bayesian source separation technique which assumes a generic model for the sources,…

Optimum linear regression in additive Cauchy-Gaussian noise

- Mathematics, Computer ScienceSignal Process.
- 2015

This work studies the estimation problem of linear regression in the presence of a new impulsive noise model, which is a sum of Cauchy and Gaussian random variables in time domain and proposes an M-estimator with the pseudo-Voigt function, which attains the CRLB.

Estimation under additive Cauchy-Gaussian noise using Markov chain Monte Carlo

- Mathematics, Computer Science2014 IEEE Workshop on Statistical Signal Processing (SSP)
- 2014

This paper considers an impulsive mixture noise process, which commonly comes across in applications such as multiuser radar communications, astrophysical imaging in the microwave range and kick detection in oil drilling, and proposes using a Markov chain Monte Carlo method, in particular the Metropolis-Hastings algorithm.

Techniques for Compact Source Extraction in CMB Maps

- Physics
- 2008

The detection of compact sources embedded in a background is a verycommon problem in many fields of astronomy. In these lecture notes, wepresent a review of different techniques developed for the…

## References

SHOWING 1-10 OF 48 REFERENCES

A statistical method for analysing observations of faint radio stars

- Physics
- 1957

The observation of faint radio sources is often limited by the angular resolving power of the radio telescope, and not by its sensitivity. Continuous recording of the output from the receiving…

Discriminating between unresolved point sources and 'negative' Sunyaev-Zel'dovich clusters in cosmic microwave background maps

- Physics
- 2003

Clusters of galaxies produce negative features at wavelengths λ > 1.25 mm in CMB maps, by means of the thermal SZ effect, while point radio sources produce positive peaks. This fact implies that a…

Contributions of Point Extragalactic Sources to the Cosmic Microwave Background Bispectrum

- Physics
- 2003

All the analyses of cosmic microwave background (CMB) temperature maps up to date show that CMB anisotropies follow a Gaussian distribution. On the other hand, astrophysical foregrounds, which hamper…

Point Sources in the Wilkinson Microwave Anisotropy Probe Sky Maps

- Physics
- 2003

We discuss point-source foregrounds for the Wilkinson Microwave Anisotropy Probe (WMAP) experiment. We consider several possible strategies for removing them and we assess how the statistics of the…

Point sources in the MAP sky maps

- Physics
- 2003

We discuss point sources foregrounds for the MAP experiment. We consider several possible strategies for removing them and we assess how the statistics of the CMB signal are affected by the residual…

Point source detection using the Spherical Mexican Hat Wavelet on simulated all-sky Planck maps

- Physics
- 2003

We present an estimation of the point source (PS) catalogue that could be extracted from the forthcoming ESA Planck mission data. We have applied the Spherical Mexican Hat Wavelet (SMHW) to simulated…

First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Tests of Gaussianity

- Physics
- 2003

We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1 yr cosmic microwave background sky maps. A nonlinear coupling parameter, fNL, characterizes the amplitude of a…

Discrete source contributions to small-scale anisotropies of the microwave background

- Physics
- 1989

The temperature fluctuations of the microwave background due to unresolved, randomly distributed sources have been computed for a wide interval of angular scales (from a few arcseconds to several…

Predictions for statistical properties of forming spheroidal galaxies

- Physics
- 2003

We show that the features of the recent astrophysically motivated model by Granato et al. are fully consistent with the available statistical measurements of galaxies at (sub)millimetre wavelengths.…

Extragalactic source counts and contributions to the anisotropies of the cosmic microwave background: predictions for the Planck Surveyor mission

- Physics
- 1998

We present predictions for the counts of extragalactic sources, the contributions to fluctuations and their angular power spectrum in each channel foreseen for the Planck Surveyor (formerly…