2005

Journal article
Open Access

Bedini L., Herranz D., Salerno E., Baccigalupi C., Kuruoglu E. E., Tonazzini A.

image processing J.2 Physical Sciences and Engineering statistical Electrical and Electronic Engineering Astrophysics Astrophysics (astro-ph) cosmic microwave background Hardware and Architecture FOS: Physical sciences I.4 Image processing and computer vision Signal Processing

This paper proposes a new strategy to separate astrophysical sources that are mutually correlated. This strategy is based on second order statistics and exploits prior information about the possible structure of the mixing matrix. Unlike ICA blind separation approaches, where the sources are assumed mutually independent and no prior knowledge is assumed about the mixing matrix, our strategy allows the independence assumption to be relaxed and performs the separation of even significantly correlated sources. Besides the mixing matrix, our strategy is also capable to evaluate the source covariance functions at several lags. Moreover, once the mixing parameters have been identified, a simple deconvolution can be used to estimate the probability density functions of the source processes. To benchmark our algorithm, we used a database that simulates the one expected from the instruments that will operate onboard ESA's Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere.

**Source: **EURASIP journal on applied signal processing 2005 (2005): 2400–2412. doi:10.1155/ASP.2005.2400

**Publisher: **Hindawi Publishing Corporation, Cairo , Egitto

[1] M. Tegmark, D. J. Eisenstein, W. Hu, and A. de Oliveira-Costa, “Foregrounds and forecasts for the cosmic microwave background,” Astrophysical Journal, vol. 530, no. 1, pp. 133-165, 2000.

[2] M. P. Hobson, A. W. Jones, A. N. Lasenby, and F. R. Bouchet, “Foreground separation methods for satellite observations of the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 300, no. 1, pp. 1-29, 1998.

[3] F. R. Bouchet, S. Prunet, and S. K. Sethi, “Multifrequency Wiener filtering of cosmic microwave background data with polarization,” Monthly Notices of the Royal Astronomical Society, vol. 302, no. 4, pp. 663-676, 1999.

[4] A. W. Jones, M. P. Hobson, P. Mukherjee, and A. N. Lasenby, “The effect of a spatially varying Galactic spectral index on the maximum entropy reconstruction of Planck Surveyor satellite data,” Astrophysical Letters & Communications, vol. 37, no. 3- 6, pp. 369-375, 2000.

[5] R. B. Barreiro, M. P. Hobson, A. J. Banday, et al., “Foreground separation using a flexible maximum-entropy algorithm: an application to COBE data,” Monthly Notices of the Royal Astronomical Society, vol. 351, no. 2, pp. 515-540, 2004.

[6] C. Baccigalupi, L. Bedini, C. Burigana, et al., “Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps,” Monthly Notices of the Royal Astronomical Society, vol. 318, no. 3, pp. 769-780, 2000.

[7] D. Maino, A. Farusi, C. Baccigalupi, et al., “All-sky astrophysical component separation with Fast Independent Component Analysis (fastica),” Monthly Notices of the Royal Astronomical Society, vol. 334, no. 1, pp. 53-68, 2002.

[8] C. Baccigalupi, F. Perrotta, G. De Zotti, et al., “Extracting cosmic microwave background polarization from satellite astrophysical maps,” Monthly Notices of the Royal Astronomical Society, vol. 354, no. 1, pp. 55-70, 2004.

[9] J. Delabrouille, J.-F. Cardoso, and G. Patanchon, “Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis,” Monthly Notices of the Royal Astronomical Society, vol. 346, no. 4, pp. 1089- 1102, 2002.

[10] A. Hyva¨rinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks, vol. 13, no. 4- 5, pp. 411-430, 2000.

[11] E. E. Kuruog˘lu, L. Bedini, M. T. Paratore, E. Salerno, and A. Tonazzini, “Source separation in astrophysical maps using independent factor analysis,” Neural Networks, vol. 16, no. 3-4, pp. 479-491, 2003.

[12] P. Comon, “Independent component analysis, a new concept?” Signal Processing, vol. 36, no. 3, pp. 287-314, 1994.

[13] J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE, vol. 86, no. 10, pp. 2009-2025, 1998.

[14] L. Tong, R.-W. Liu, V. C. Soon, and Y.-F. Huang, “Indeterminacy and identifiability of blind identification,” IEEE Trans. Circuits Syst., vol. 38, no. 5, pp. 499-509, 1991.

[15] A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines, “A blind source separation technique using secondorder statistics,” IEEE Trans. Signal Processing, vol. 45, no. 2, pp. 434-444, 1997.

[16] E. Salerno, C. Baccigalupi, L. Bedini, et al., “Independent component analysis approach to detect the cosmic microwave background radiation from satellite measurements,” Tech. Rep. B4-04, IEI-CNR, Pisa, Italy, 2000.

[17] G. Patanchon, H. Snoussi, J.-F. Cardoso, and J. Delabrouille, “Component separation for Cosmic Microwave Background data: a blind approach based on spectral diversity,” in Proc. 3rd Workshop on Physics in Signal and Image Processing (PSIP '03), pp. 17-20, Grenoble, France, January 2003.

[18] G. De Zotti, L. Toffolatti, F. Arg u¨eso, et al., “The planck surveyor mission: astrophysical prospects,” in 3K Cosmology, Proc. EC-TMR Conference, vol. 476, pp. 204-204, American Institute of Physics, Rome, Italy, October 1999.

[19] P. Vielva, E. Mart´ınez-Gonza´lez, L. Cayo´ n, J. M. Diego, J. L. Sanz, and L. Toffolatti, “Predicted Planck extragalactic pointsource catalogue,” Monthly Notices of the Royal Astronomical Society, vol. 326, no. 1, pp. 181-191, 2001.

[20] L. Tenorio, A. H. Jaffe, S. Hanany, and C. H. Lineweaver, “Applications of wavelets to the analysis of cosmic microwave background maps,” Monthly Notices of the Royal Astronomical Society, vol. 310, no. 3, pp. 823-834, 1999.

[21] L. Cayo´ n, J. L. Sanz, R. B. Barreiro, et al., “Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background maps,” Monthly Notices of the Royal Astronomical Society, vol. 315, no. 4, pp. 757-761, 2000.

[22] A. K. Barros and A. Cichocki, “Extraction of specific signals with temporal structure,” Neural Computation, vol. 13, no. 9, pp. 1995-2004, 2001.

[23] L. Bedini, S. Bottini, C. Baccigalupi, et al., “A semi-blind approach for statistical source separation in astrophysical maps,” Tech. Rep. ISTI-2003-TR-35, ISTI-CNR, Pisa, Italy, 2003.

[24] E. Moulines, J.-F. Cardoso, and E. Gassiat, “Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP '97), vol. 5, pp. 3617-3620, Munich, Germany, April 1997.

[25] H. Attias, “Independent factor analysis,” Neural Computation, vol. 11, no. 4, pp. 803-851, 1999.

[26] A. J. Banday and A. W. Wolfendale, “Galactic dust emission and the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 252, pp. 462-472, 1991.

[27] G. Giardino, A. J. Banday, K. M. Go´ rski, K. Bennett, J. L. Jonas, and J. Tauber, “Towards a model of full-sky Galactic synchrotron intensity and linear polarisation: a re-analysis of the Parkes data,” Astronomy & Astrophysics, vol. 387, no. 1, pp. 82-97, 2002.

[28] C. L. Bennett, R. S. Hill, G. Hinshaw, et al., “First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Foreground emission,” Astrophysical Journal Supplement Series, vol. 148, no. 1, pp. 97-117, 2003.

[29] A. K. Barros, “Dependent component analysis,” in Advances in Independent Component Analysis, M. Girolami, Ed., Springer, New York, NY, USA, July 2000.

L. Bedini graduated cum laude in electronic engineering from the University of Pisa, Italy, in 1968. Since 1970, he has been a researcher of the Italian National Research Council, Istituto di Scienza e Tecnologie dell'Informazione, Pisa, Italy. His interests have been in modelling, identification, and parameter estimation of biological systems applied to noninvasive diagnostic techniques. At present, his research interest is in the field of digital signal processing, image reconstruction, and neural networks applied to image processing. He is a coauthor of more than 80 scientific papers. From 1971 to 1989, he was an Associate Professor of system theory at the Computer Science Department, University of Pisa, Italy.

D. Herranz received the B.S. degree in 1995 and the M.S. degree in 1995 from the Universidad Complutense de Madrid, Madrid, Spain, and the Ph.D. degree in astrophysics from Universidad de Cantabria, Santander, Spain, in 2002. He was a CMBNET Postdoctoral Fellow at the Istituto di Scienza e Tecnologie dell'Informazione “A. Faedo” (CNR), Pisa, Italy, from 2002 to 2004. He is currently at the Instituto de Fisica de Cantabria, Santander, Spain, under an MEC Juan de la Cierva contract. His research interests are in the areas of cosmic microwave background astronomy and extragalactic point source statistics as well as the application of statistical signal processing to astronomical data, including blind source separation, linear and nonlinear data filtering, and statistical modeling of heavy-tailed processes.

[1] Amari S., Chichocki A., 1998, “Adaptive Blind Signal Processing - Neural Network Approaches”, Proc. IEEE, 86, 2026-2048

[2] Attias H., 1999, “Independent factor analysis”, Neural Computation, 11, 803-851

[3] Baccigalupi C., Bedini L., Burigana C., et al., 2000, “Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps”, MNRAS, 318, 769-780

[4] Baccigalupi C., Perrotta F., De Zotti G., et al., 2002, “Extracting cosmic microwave background polarisation from satellite astrophysical maps”, astro-ph/0209591

[5] Banday A. J., Wolfendale A. W., 1991, “Galactic dust emission and the cosmic microwave abclground”, MNRAS 252, 462-472

[6] Barreiro R. B., Hobson M. P., Banday A. J., et al., 2003, “Foreground separation using a flexible maximum-entropy algorithm: an application to COBE data”, astro-ph/0302091

[7] Barros A. K., 2000, “Dependent component analysis”, in Girolami M. (Ed.), Advances in Independent Component Analysis, Springer, 63

[8] Barros A. K., Cichocki A., 2001, “Extraction of specific signals with temporal structure”, Neural Computation, 13, 1995-2003

[9] Bedini L., Bottini S., Baccigalupi C., et al., 2003, “A semi-blind approach for statistical source separation in astrophysical maps”, ISTI-CNR, Pisa, Italy, Technical Report ISTI-2003-TR-35

[10] Belouchrani A., Abed-Meraim K., Cardoso J.-F., Moulines E., 1997, “A blind source separation technique based on second order statistics”, IEEE Trans. on SP, 45, 434-444

[11] Bennett C., Hill, R. S., Hinshaw G., et al., 2003, “First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Foreground emission”, ApJ, supplement series, 148, 97-117

[12] Bouchet F. R., Prunet S., Sethi S. K., 1999, “Multifrequency Wiener filtering of cosmic microwave background data with polarization”, MNRAS, 302, 663-676

[13] Cardoso J.-F., 1998, “Blind signal separation: statistical principles”, Proc. IEEE, 86, 2009-2025

[14] Cay´on L., Sanz J. L., Barreiro R. B., et al., 2000, “Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background map”, MNRAS, 315, 757-761

[15] Comon P., 1994, “Independent Component Analysis, A New Concept?”, Signal Processing, 36, 287-314

[16] Delabrouille J., Cardoso J.-F., Patanchon G., 2002, “Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis”, MNRAS, 346, 1089-1102

[17] De Zotti G., Toffolatti L., Argu¨eso F., et al., 1999, “The Planck Surveyor Mission: Astrophysical Prospects”, 3K Cosmology, Proc. of the EC-TMR Conference, Woodbury, NY, American Institute of Physics, 476, 204

[18] Giardino G. A., Banday A. J., G´orski K. M., Bennett K., Jonas J. L., Tauber J., 2002, “Towards a model of full-sky Galactic synchrotron intensity and linear polarisation: A re-analysis of the Parkes data”, A&A 387, 82-97

[19] Hobson M. P., Jones A. W., Lasenby A. N., Bouchet F. R., 1998, “Foreground separation methods for satellite observations of the cosmic microwave background”, MNRAS, 300, 1-29

[20] Hyv¨arinen A., Oja E., 2000, “Independent component analysis: algorithms and applications”, Neural Networks, 13, 411-430

[21] Jones A. W., Hobson M. P., Mukherjee P., Lasenby A. N., 2000, “The effect of a spatially varying Galactic spectral index on the maximum entropy reconstruction of Planck Surveyor satellite data”, APL&C, 37, 369-375

[22] Kuruog˘lu E.E., Bedini L., Paratore M. T., Salerno E., Tonazzini A., 2003, “Source separation in astrophysical maps using independent factor analysis”, Neural Networks, 16, 479-491

[23] Maino D., Farusi A., Baccigalupi C., et al., 2002, “All-sky astrophysical component separation with Fast Independent Component Analysis (FastICA)”, MNRAS, 334, 53-68

[24] Moulines E., Cardoso J. F., Gassiat E., 1997, “Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models”, Proc. ICASSP'97, 5, 3617-3620

[25] Patanchon G., Snoussi H., Cardoso J.-F., Delabrouille J., 2003, “Component separation for Cosmic Microwave Background data: a blind approach based on spectral diversity”, astro-ph/0302078

[26] Salerno E., Baccigalupi C., Bedini L., et al., 2000, “Independent Component Analysis Approach to Detect the Cosmic Microwave Background Radiation from Satellite Measurements”, IEI-CNR, Pisa, Italy, Technical Report B4-04

[27] Tegmark M., Eisenstein D. J., Hu W., de Oliveira-Costa A., 2000, “Foregrounds and forecasts for the cosmic microwave background”, ApJ, 530, 133- 165

[28] Tenorio L., Jaffe A. H., Hanany S., Lineweaver C. H., 1999, “Applications of wavelets to the analysis of cosmic microwave background maps”, MNRAS, 310, 823-834

[29] Tong L., Liu R., Soon V. C., Huang Y.-F., 1991, “Indeterminacy and identifiability of blind identification”, IEEE Trans. on CAS, 38, 499-509

[30] Vielva P., Mart´ınez-Gonza´lez E., Cay´on L., Diego J. M., Sanz J. L., Toffolatti L., 2001, “Predicted Planck extragalactic point-source catalogue”, MNRAS, 326, 181-191

[31] Yeredor A., 2002, “Non-orthogonal joint diagonalization in the leat-squares sense with application in blind source separation”, IEEE Trans. on SP, 50, 1545-1553

[2] M. P. Hobson, A. W. Jones, A. N. Lasenby, and F. R. Bouchet, “Foreground separation methods for satellite observations of the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 300, no. 1, pp. 1-29, 1998.

[3] F. R. Bouchet, S. Prunet, and S. K. Sethi, “Multifrequency Wiener filtering of cosmic microwave background data with polarization,” Monthly Notices of the Royal Astronomical Society, vol. 302, no. 4, pp. 663-676, 1999.

[4] A. W. Jones, M. P. Hobson, P. Mukherjee, and A. N. Lasenby, “The effect of a spatially varying Galactic spectral index on the maximum entropy reconstruction of Planck Surveyor satellite data,” Astrophysical Letters & Communications, vol. 37, no. 3- 6, pp. 369-375, 2000.

[5] R. B. Barreiro, M. P. Hobson, A. J. Banday, et al., “Foreground separation using a flexible maximum-entropy algorithm: an application to COBE data,” Monthly Notices of the Royal Astronomical Society, vol. 351, no. 2, pp. 515-540, 2004.

[6] C. Baccigalupi, L. Bedini, C. Burigana, et al., “Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps,” Monthly Notices of the Royal Astronomical Society, vol. 318, no. 3, pp. 769-780, 2000.

[7] D. Maino, A. Farusi, C. Baccigalupi, et al., “All-sky astrophysical component separation with Fast Independent Component Analysis (fastica),” Monthly Notices of the Royal Astronomical Society, vol. 334, no. 1, pp. 53-68, 2002.

[8] C. Baccigalupi, F. Perrotta, G. De Zotti, et al., “Extracting cosmic microwave background polarization from satellite astrophysical maps,” Monthly Notices of the Royal Astronomical Society, vol. 354, no. 1, pp. 55-70, 2004.

[9] J. Delabrouille, J.-F. Cardoso, and G. Patanchon, “Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis,” Monthly Notices of the Royal Astronomical Society, vol. 346, no. 4, pp. 1089- 1102, 2002.

[10] A. Hyva¨rinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks, vol. 13, no. 4- 5, pp. 411-430, 2000.

[11] E. E. Kuruog˘lu, L. Bedini, M. T. Paratore, E. Salerno, and A. Tonazzini, “Source separation in astrophysical maps using independent factor analysis,” Neural Networks, vol. 16, no. 3-4, pp. 479-491, 2003.

[12] P. Comon, “Independent component analysis, a new concept?” Signal Processing, vol. 36, no. 3, pp. 287-314, 1994.

[13] J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE, vol. 86, no. 10, pp. 2009-2025, 1998.

[14] L. Tong, R.-W. Liu, V. C. Soon, and Y.-F. Huang, “Indeterminacy and identifiability of blind identification,” IEEE Trans. Circuits Syst., vol. 38, no. 5, pp. 499-509, 1991.

[15] A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines, “A blind source separation technique using secondorder statistics,” IEEE Trans. Signal Processing, vol. 45, no. 2, pp. 434-444, 1997.

[16] E. Salerno, C. Baccigalupi, L. Bedini, et al., “Independent component analysis approach to detect the cosmic microwave background radiation from satellite measurements,” Tech. Rep. B4-04, IEI-CNR, Pisa, Italy, 2000.

[17] G. Patanchon, H. Snoussi, J.-F. Cardoso, and J. Delabrouille, “Component separation for Cosmic Microwave Background data: a blind approach based on spectral diversity,” in Proc. 3rd Workshop on Physics in Signal and Image Processing (PSIP '03), pp. 17-20, Grenoble, France, January 2003.

[18] G. De Zotti, L. Toffolatti, F. Arg u¨eso, et al., “The planck surveyor mission: astrophysical prospects,” in 3K Cosmology, Proc. EC-TMR Conference, vol. 476, pp. 204-204, American Institute of Physics, Rome, Italy, October 1999.

[19] P. Vielva, E. Mart´ınez-Gonza´lez, L. Cayo´ n, J. M. Diego, J. L. Sanz, and L. Toffolatti, “Predicted Planck extragalactic pointsource catalogue,” Monthly Notices of the Royal Astronomical Society, vol. 326, no. 1, pp. 181-191, 2001.

[20] L. Tenorio, A. H. Jaffe, S. Hanany, and C. H. Lineweaver, “Applications of wavelets to the analysis of cosmic microwave background maps,” Monthly Notices of the Royal Astronomical Society, vol. 310, no. 3, pp. 823-834, 1999.

[21] L. Cayo´ n, J. L. Sanz, R. B. Barreiro, et al., “Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background maps,” Monthly Notices of the Royal Astronomical Society, vol. 315, no. 4, pp. 757-761, 2000.

[22] A. K. Barros and A. Cichocki, “Extraction of specific signals with temporal structure,” Neural Computation, vol. 13, no. 9, pp. 1995-2004, 2001.

[23] L. Bedini, S. Bottini, C. Baccigalupi, et al., “A semi-blind approach for statistical source separation in astrophysical maps,” Tech. Rep. ISTI-2003-TR-35, ISTI-CNR, Pisa, Italy, 2003.

[24] E. Moulines, J.-F. Cardoso, and E. Gassiat, “Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP '97), vol. 5, pp. 3617-3620, Munich, Germany, April 1997.

[25] H. Attias, “Independent factor analysis,” Neural Computation, vol. 11, no. 4, pp. 803-851, 1999.

[26] A. J. Banday and A. W. Wolfendale, “Galactic dust emission and the cosmic microwave background,” Monthly Notices of the Royal Astronomical Society, vol. 252, pp. 462-472, 1991.

[27] G. Giardino, A. J. Banday, K. M. Go´ rski, K. Bennett, J. L. Jonas, and J. Tauber, “Towards a model of full-sky Galactic synchrotron intensity and linear polarisation: a re-analysis of the Parkes data,” Astronomy & Astrophysics, vol. 387, no. 1, pp. 82-97, 2002.

[28] C. L. Bennett, R. S. Hill, G. Hinshaw, et al., “First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Foreground emission,” Astrophysical Journal Supplement Series, vol. 148, no. 1, pp. 97-117, 2003.

[29] A. K. Barros, “Dependent component analysis,” in Advances in Independent Component Analysis, M. Girolami, Ed., Springer, New York, NY, USA, July 2000.

L. Bedini graduated cum laude in electronic engineering from the University of Pisa, Italy, in 1968. Since 1970, he has been a researcher of the Italian National Research Council, Istituto di Scienza e Tecnologie dell'Informazione, Pisa, Italy. His interests have been in modelling, identification, and parameter estimation of biological systems applied to noninvasive diagnostic techniques. At present, his research interest is in the field of digital signal processing, image reconstruction, and neural networks applied to image processing. He is a coauthor of more than 80 scientific papers. From 1971 to 1989, he was an Associate Professor of system theory at the Computer Science Department, University of Pisa, Italy.

D. Herranz received the B.S. degree in 1995 and the M.S. degree in 1995 from the Universidad Complutense de Madrid, Madrid, Spain, and the Ph.D. degree in astrophysics from Universidad de Cantabria, Santander, Spain, in 2002. He was a CMBNET Postdoctoral Fellow at the Istituto di Scienza e Tecnologie dell'Informazione “A. Faedo” (CNR), Pisa, Italy, from 2002 to 2004. He is currently at the Instituto de Fisica de Cantabria, Santander, Spain, under an MEC Juan de la Cierva contract. His research interests are in the areas of cosmic microwave background astronomy and extragalactic point source statistics as well as the application of statistical signal processing to astronomical data, including blind source separation, linear and nonlinear data filtering, and statistical modeling of heavy-tailed processes.

[1] Amari S., Chichocki A., 1998, “Adaptive Blind Signal Processing - Neural Network Approaches”, Proc. IEEE, 86, 2026-2048

[2] Attias H., 1999, “Independent factor analysis”, Neural Computation, 11, 803-851

[3] Baccigalupi C., Bedini L., Burigana C., et al., 2000, “Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps”, MNRAS, 318, 769-780

[4] Baccigalupi C., Perrotta F., De Zotti G., et al., 2002, “Extracting cosmic microwave background polarisation from satellite astrophysical maps”, astro-ph/0209591

[5] Banday A. J., Wolfendale A. W., 1991, “Galactic dust emission and the cosmic microwave abclground”, MNRAS 252, 462-472

[6] Barreiro R. B., Hobson M. P., Banday A. J., et al., 2003, “Foreground separation using a flexible maximum-entropy algorithm: an application to COBE data”, astro-ph/0302091

[7] Barros A. K., 2000, “Dependent component analysis”, in Girolami M. (Ed.), Advances in Independent Component Analysis, Springer, 63

[8] Barros A. K., Cichocki A., 2001, “Extraction of specific signals with temporal structure”, Neural Computation, 13, 1995-2003

[9] Bedini L., Bottini S., Baccigalupi C., et al., 2003, “A semi-blind approach for statistical source separation in astrophysical maps”, ISTI-CNR, Pisa, Italy, Technical Report ISTI-2003-TR-35

[10] Belouchrani A., Abed-Meraim K., Cardoso J.-F., Moulines E., 1997, “A blind source separation technique based on second order statistics”, IEEE Trans. on SP, 45, 434-444

[11] Bennett C., Hill, R. S., Hinshaw G., et al., 2003, “First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Foreground emission”, ApJ, supplement series, 148, 97-117

[12] Bouchet F. R., Prunet S., Sethi S. K., 1999, “Multifrequency Wiener filtering of cosmic microwave background data with polarization”, MNRAS, 302, 663-676

[13] Cardoso J.-F., 1998, “Blind signal separation: statistical principles”, Proc. IEEE, 86, 2009-2025

[14] Cay´on L., Sanz J. L., Barreiro R. B., et al., 2000, “Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background map”, MNRAS, 315, 757-761

[15] Comon P., 1994, “Independent Component Analysis, A New Concept?”, Signal Processing, 36, 287-314

[16] Delabrouille J., Cardoso J.-F., Patanchon G., 2002, “Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis”, MNRAS, 346, 1089-1102

[17] De Zotti G., Toffolatti L., Argu¨eso F., et al., 1999, “The Planck Surveyor Mission: Astrophysical Prospects”, 3K Cosmology, Proc. of the EC-TMR Conference, Woodbury, NY, American Institute of Physics, 476, 204

[18] Giardino G. A., Banday A. J., G´orski K. M., Bennett K., Jonas J. L., Tauber J., 2002, “Towards a model of full-sky Galactic synchrotron intensity and linear polarisation: A re-analysis of the Parkes data”, A&A 387, 82-97

[19] Hobson M. P., Jones A. W., Lasenby A. N., Bouchet F. R., 1998, “Foreground separation methods for satellite observations of the cosmic microwave background”, MNRAS, 300, 1-29

[20] Hyv¨arinen A., Oja E., 2000, “Independent component analysis: algorithms and applications”, Neural Networks, 13, 411-430

[21] Jones A. W., Hobson M. P., Mukherjee P., Lasenby A. N., 2000, “The effect of a spatially varying Galactic spectral index on the maximum entropy reconstruction of Planck Surveyor satellite data”, APL&C, 37, 369-375

[22] Kuruog˘lu E.E., Bedini L., Paratore M. T., Salerno E., Tonazzini A., 2003, “Source separation in astrophysical maps using independent factor analysis”, Neural Networks, 16, 479-491

[23] Maino D., Farusi A., Baccigalupi C., et al., 2002, “All-sky astrophysical component separation with Fast Independent Component Analysis (FastICA)”, MNRAS, 334, 53-68

[24] Moulines E., Cardoso J. F., Gassiat E., 1997, “Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models”, Proc. ICASSP'97, 5, 3617-3620

[25] Patanchon G., Snoussi H., Cardoso J.-F., Delabrouille J., 2003, “Component separation for Cosmic Microwave Background data: a blind approach based on spectral diversity”, astro-ph/0302078

[26] Salerno E., Baccigalupi C., Bedini L., et al., 2000, “Independent Component Analysis Approach to Detect the Cosmic Microwave Background Radiation from Satellite Measurements”, IEI-CNR, Pisa, Italy, Technical Report B4-04

[27] Tegmark M., Eisenstein D. J., Hu W., de Oliveira-Costa A., 2000, “Foregrounds and forecasts for the cosmic microwave background”, ApJ, 530, 133- 165

[28] Tenorio L., Jaffe A. H., Hanany S., Lineweaver C. H., 1999, “Applications of wavelets to the analysis of cosmic microwave background maps”, MNRAS, 310, 823-834

[29] Tong L., Liu R., Soon V. C., Huang Y.-F., 1991, “Indeterminacy and identifiability of blind identification”, IEEE Trans. on CAS, 38, 499-509

[30] Vielva P., Mart´ınez-Gonza´lez E., Cay´on L., Diego J. M., Sanz J. L., Toffolatti L., 2001, “Predicted Planck extragalactic point-source catalogue”, MNRAS, 326, 181-191

[31] Yeredor A., 2002, “Non-orthogonal joint diagonalization in the leat-squares sense with application in blind source separation”, IEEE Trans. on SP, 50, 1545-1553

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@article{oai:it.cnr:prodotti:43838, title = {Separation of correlated astrophysical sources using multiple-lag data covariance matrices}, author = {Bedini L. and Herranz D. and Salerno E. and Baccigalupi C. and Kuruoglu E. E. and Tonazzini A.}, publisher = {Hindawi Publishing Corporation, Cairo , Egitto}, doi = {10.1155/asp.2005.2400 and 10.48550/arxiv.astro-ph/0407108}, journal = {EURASIP journal on applied signal processing}, volume = {2005}, pages = {2400–2412}, year = {2005} }