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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Blind Component Separation in Wavelet Space: Application to CMB Analysis | EURASIP Journal on Applied Signal Processing 2005 15 2437-2454 2005 Hindawi Publishing Corporation Blind Component Separation in Wavelet Space Application to CMB Analysis Y. Moudden DAPNIA SEDI-SAP CEA Saclay 91191 Gif-sur-Yvette France Email yassir.moudden@cea.fr J.-F. Cardoso CNRS Ecole National Superieure des Telecommunications 46 rue Barrault 75634 Paris France Email cardoso@tsi.enst.fr J.-L. Starck DAPNIA SEDI-SAP CEA Saclay 91191 Gif-sur-Yvette France Email jstarck@cea.fr J. Delabrouille CNRS PCC College de France 11 place Marcelin Berthelot 75231 Paris France Email delabrouille@cdf.in2p3.fr Received 30 June 2004 Revised 22 November 2004 It is a recurrent issue in astronomical data analysis that observations are incomplete maps with missing patches or intentionally masked parts. In addition many astrophysical emissions are nonstationary processes over the sky. All these effects impair data processing techniques which work in the Fourier domain. Spectral matching ICA SMICA is a source separation method based on spectral matching in Fourier space designed for the separation of diffuse astrophysical emissions in cosmic microwave background observations. This paper proposes an extension of SMICA to the wavelet domain and demonstrates the effectiveness of waveletbased statistics for dealing with gaps in the data. Keywords and phrases blind source separation cosmic microwave background wavelets data analysis missing data. 1. INTRODUCTION The detection of cosmic microwave background CMB anisotropies on the sky has been over the past three decades a subject of intense activity in the cosmology community. The CMB discovered in 1965 by Penzias and Wilson is a relic radiation emitted some 13 billion years ago when the universe was about 370 000 years old. Small fluctuations of this emission tracing the seeds of the primordial inhomogeneities which gave rise to present large scale structures as galaxies and clusters of galaxies were first discovered in the observations .