Astrophysical image separation by blind time-frequency source separation methods

In this paper, two prevalent blind time-frequency (TF) source separation methods in the literature are adapted to astrophysical image mixtures and four algorithms are developed to separate them into their astrophysical components. The components considered in this work are cosmic microwave background (CMB) radiation, galactic dust and synchrotron, among which the CMB component is emphasized. These simulated components mixed via realistic coefficients are subjected to simulated additive, nonstationary Gaussian noise components of realistic power levels, to yield image mixtures on which our orthogonal and nonorthogonal TF algorithms are applied. The developed algorithms are compared with the FastICA algorithm and CMB component is found to be recovered with an improvement reaching to 3.25 decibels from CMB-synchrotron mixtures. The proposed techniques are believed to be generically applicable in separating other types of astrophysical components as well.

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

[2]  Hicham Ghennioui,et al.  Nonorthogonal joint diagonalization of spatial quadratic time-frequency matrices for source separation , 2005, IEEE Signal Processing Letters.

[3]  Albert H. Nuttall.  Alias-Free Wigner Distribution Function and Complex Ambiguity Function for Discrete-Time Samples , 1989 .

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

[5]  Moeness G. Amin,et al.  Blind source separation based on time-frequency signal representations , 1998, IEEE Trans. Signal Process..

[6]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[7]  Antonia Papandreou-Suppappola,et al.  Applications in Time-Frequency Signal Processing , 2002 .

[8]  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.

[9]  F. Hlawatsch,et al.  Linear Time–Frequency Filters: On-line Algorithms and Applications , 2018, Applications in Time-Frequency Signal Processing.

[10]  E. Salerno,et al.  Source separation in astrophysical maps using independent factor analysis , 2003 .

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

[12]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

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

[14]  Klaus Obermayer,et al.  Quadratic optimization for simultaneous matrix diagonalization , 2006, IEEE Transactions on Signal Processing.

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

[16]  Patrick Flandrin,et al.  Some features of time-frequency representations of multicomponent signals , 1984, ICASSP.

[17]  L. Toffolatti,et al.  Comparison of filters for the detection of point sources in Planck simulations , 2006 .

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

[19]  Arie Yeredor,et al.  On using exact joint diagonalization for noniterative approximate joint diagonalization , 2005, IEEE Signal Processing Letters.

[20]  El Mostafa Fadaili,et al.  Nonorthogonal Joint Diagonalization/Zero Diagonalization for Source Separation Based on Time-Frequency Distributions , 2007, IEEE Transactions on Signal Processing.

[21]  Xi-Lin Li,et al.  Nonorthogonal Joint Diagonalization Free of Degenerate Solution , 2007, IEEE Transactions on Signal Processing.

[22]  Serge Dégerine,et al.  A Comparative Study of Approximate Joint Diagonalization Algorithms for Blind Source Separation in Presence of Additive Noise , 2007, IEEE Transactions on Signal Processing.