Bayesian source separation for cosmology

Recent satellite missions have provided and continue to provide us with vast amounts of data on radiation measurements that generally present themselves as superpositions of various cosmological sources, most importantly cosmic microwave background (CMB) radiation and other galactic and extragalactic sources. We would like to obtain the estimates of these sources separately since they carry vital information of cosmological significance about our Universe. Although initial attempts to obtain sources have utilized blind estimation techniques, the presence of important astrophysical prior information and the demanding nature of the problem makes the use of informed techniques possible and indispensable. In this article, our objective is to present a formulation of the problem in Bayesian framework for the signal processing community and to provide a panorama of Bayesian source separation techniques for the estimation of cosmological components from the observation mixtures.

[1]  J. Cardoso,et al.  Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis , 2002, astro-ph/0211504.

[2]  Patricio Vielva,et al.  Cosmic microwave background images , 2011, IEEE Signal Processing Magazine.

[3]  Bülent Sankur,et al.  Fast MCMC separation for MRF modelled astrophysical components , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[4]  Kevin H. Knuth,et al.  Informed source separation: A Bayesian tutorial , 2013, 2005 13th European Signal Processing Conference.

[5]  Simon P. Wilson,et al.  Fully Bayesian Source Separation of Astrophysical Images Modelled by Mixture of Gaussians , 2008, IEEE Journal of Selected Topics in Signal Processing.

[6]  H. Snoussi,et al.  Bayesian blind component separation for Cosmic Microwave Background observations , 2001 .

[7]  H. K. Eriksen,et al.  Power Spectrum Estimation from High-Resolution Maps by Gibbs Sampling , 2004 .

[8]  C. H. Anderson,et al.  Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background , 2002, astro-ph/0209560.

[9]  W. N. Brandt,et al.  Separation of Foreground Radiation from Cosmic Microwave Background Anisotropy Using Multifrequency Measurements , 1994 .

[10]  A. Doucet.  On sequential Monte Carlo methods for Bayesian filtering , 1998 .

[11]  Albert Bijaoui,et al.  Blind source separation and analysis of multispectral astronomical images , 2000 .

[12]  Kevin H. Knuth.  A Bayesian approach to source separation , 1999 .

[13]  P. Lilje,et al.  Bayesian Power Spectrum Analysis of the First-Year WMAP data , 2004, astro-ph/0407027.

[14]  Benjamin D. Wandelt,et al.  Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling , 2004 .

[15]  Shun-ichi Amari,et al.  Adaptive blind signal processing-neural network approaches , 1998, Proc. IEEE.

[16]  N. Christensen,et al.  Bayesian methods for cosmological parameter estimation from cosmic microwave background measurements , 2000, astro-ph/0103134.

[17]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[20]  P. Lilje,et al.  Bayesian Power Spectrum Analysis of the First-Year Wilkinson Microwave Anisotropy Probe Data , 2004 .

[21]  M. Hobson,et al.  Fast optimal CMB power spectrum estimation with Hamiltonian sampling , 2007, 0708.2989.

[22]  D. Herranz,et al.  Separation of Noisy Astrophysical Images by Blind Time-Frequency Source Separation Methods , 2007, 2007 IEEE 15th Signal Processing and Communications Applications.

[23]  Joanne Cohn,et al.  Resource Letter: TACMB-1: The theory of anisotropies in the cosmic microwave background , 2002 .

[24]  Anna Tonazzini,et al.  Source separation in noisy astrophysical images modelled by Markov random fields , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[25]  C. Baccigalupi,et al.  Estimating the spectral indices of correlated astrophysical foregrounds by a second-order statistical approach , 2006, astro-ph/0609701.

[26]  Ercan E. Kuruoglu,et al.  Image separation using particle filters , 2007, Digit. Signal Process..

[27]  Hichem Snoussi,et al.  Blind separation of noisy Gaussian stationary sources. Application to cosmic microwave background imaging , 2002, 2002 11th European Signal Processing Conference.

[28]  J. Fadili,et al.  SZ and CMB reconstruction using generalized morphological component analysis , 2007, 0712.0588.

[29]  M. Halpern,et al.  First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity , 2003 .

[30]  Bülent Sankur,et al.  Bayesian Separation of Images Modeled With MRFs Using MCMC , 2009, IEEE Transactions on Image Processing.

[31]  Jean-Luc Starck,et al.  Blind Component Separation in Wavelet Space: Application to CMB Analysis , 2005, EURASIP J. Adv. Signal Process..

[32]  M. Hobson,et al.  All-sky component separation for the Planck mission , 2001, astro-ph/0105432.

[33]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[34]  G. Zotti,et al.  All-sky astrophysical component separation with Fast Independent Component Analysis (FastICA) , 2001, astro-ph/0108362.

[35]  Walter R. Gilks,et al.  Strategies for improving MCMC , 1995 .

[36]  Ercan E. Kuruoglu,et al.  Astrophysical Source Separation Using Particle Filters , 2004, ICA.

[37]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[38]  Ercan Kuruoǧlu.  Bayesian Separation of Independent Sources in Astrophysical Radiation Maps Using MCMC , 2003 .

[39]  A. Lasenby,et al.  Foreground separation methods for satellite observations of the cosmic microwave background , 1998, astro-ph/9806387.

[40]  C. Baccigalupi,et al.  Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps , 2000, astro-ph/0002257.

[41]  Anna Tonazzini,et al.  Source separation in astrophysical maps using independent factor analysis , 2003, Neural Networks.

[42]  R. B. Barreiro,et al.  Component separation methods for the PLANCK mission , 2008, 0805.0269.

[43]  Michael Seiffert,et al.  Cosmic Microwave Background Component Separation by Parameter Estimation , 2005, astro-ph/0508268.

[44]  K. Gorski,et al.  A MARKOV CHAIN MONTE CARLO ALGORITHM FOR ANALYSIS OF LOW SIGNAL-TO-NOISE COSMIC MICROWAVE BACKGROUND DATA , 2008, 0807.0624.

[45]  Ercan E. Kuruoglu,et al.  Astrophysical image separation by blind time-frequency source separation methods , 2009, Digit. Signal Process..

[46]  H. K. Eriksen,et al.  Joint Bayesian Component Separation and CMB Power Spectrum Estimation , 2007, 0709.1058.

[47]  J. Cardoso,et al.  Cosmic microwave background and foregrounds in Wilkinson Microwave Anisotropy Probe first-year data , 2005 .

[48]  S. Dodelson,et al.  Cosmic Microwave Background Anisotropies , 2001, astro-ph/0110414.

[49]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[50]  A. N. Lasenby,et al.  All-sky component separation in the presence of anisotropic noise and dust temperature variations , 2004 .

[51]  C. G. T. Haslam,et al.  A 408 MHz all-sky continuum survey. II. The atlas of contour maps. , 1982 .

[52]  J. Jewell,et al.  Bayesian Approach to Foreground Removal , 1999 .

[53]  J. D. Doll,et al.  Brownian dynamics as smart Monte Carlo simulation , 1978 .

[54]  H. K. Eriksen,et al.  Preprint typeset using L ATEX style emulateapj v. 6/22/04 CMB COMPONENT SEPARATION BY PARAMETER ESTIMATION , 2008 .

[55]  Anna Tonazzini,et al.  Separation of Correlated Astrophysical Sources Using Multiple-Lag Data Covariance Matrices , 2005, EURASIP J. Adv. Signal Process..