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Analysis of Astrophysical Data Cubes using Cross-correlations and Wavelet Denoisings

Analysis of Astrophysical Data Cubes using Cross-correlations and Wavelet Denoisings. A.Bijaoui 1 , D.Mékarnia 1 , J.P.Maillard 2 , C.Delle Luche 1 1 Observatoire de la Côte d'Azur (Nice) 2 Institut d’Astrophysique de Paris. Outlines. The A strophysical Data Cubes BEAR and IFTS

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Analysis of Astrophysical Data Cubes using Cross-correlations and Wavelet Denoisings

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  1. Analysis of Astrophysical Data Cubes using Cross-correlations and Wavelet Denoisings A.Bijaoui1, D.Mékarnia1, J.P.Maillard2, C.Delle Luche1 1 Observatoire de la Côte d'Azur (Nice) 2 Institut d’Astrophysique de Paris Granada iAstro Worshop

  2. Outlines • The Astrophysical Data Cubes • BEAR and IFTS • The Karhunen-Loève expansion (KL/PCA) • The KL basis • The noise of the basis /components • Wavelet denoising of the basis/components • The residues and their denoising • An application on NGC 7027 cube • Conclusion Granada iAstro Worshop

  3. The Integral-Field Spectrographs • Different optical devices • Scanning Fabry-Perot • Optical fibers (VIMOS, GIRAFFE) • Cylindrical lenses + Grating (TIGRE, OASIS) • Multislit (SAURON, MUSE) • Imaging Fourier Transform Spectrograph • Resulting Data Cubes • Size depending on the device • From Megapixel to Gigapixel • Need of specific analysis methods Granada iAstro Worshop

  4. BEAR : an IFTS device Granada iAstro Worshop

  5. BEAR at the CFHT focus Granada iAstro Worshop

  6. The example of NGC 7027 • A post AGB planetary nebula • Observations  Cox et al. 2002 • The resampled data cube: 128x128x1024 • What information? • Different spectral lines  Abundance • Velocity field  3D view • Continuum • Necessity to denoise the data cube • To increase the SNR • To observe fainter objects Granada iAstro Worshop

  7. The data cube Granada iAstro Worshop

  8. Spectra sample Granada iAstro Worshop

  9. Elements of the data reduction • We can take into account • The cross correlation between the images  PCA / KL expansion • The significant details image / image • The significant details spectrum / spectrum • Different possible ways • Wavelet Transform + KL exp. + Denoising + Reconstruction (Starck et al. 2001) • KL exp. + Denoising + Reconstruction + Residue + Denoising (Mékarnia et al. 2003) Granada iAstro Worshop

  10. KL and PCA • Search of uncorrelated images • The Principal Component Analysis • Iterative extraction of the linear combinations having the greatest variance • PCA application to images  KL • The eigenvalue = the energy / order Granada iAstro Worshop

  11. The noisy KL basis Granada iAstro Worshop

  12. Denoising the KL expansion • Each KL component is noisy • Depends on the order / eigenvalue • Each KL spectrum is noisy • The reconstruction from noisy components leads to a noisy restoration • Each KL component / spectrum is denoised • Wavelet denoising • Redundant transform • Soft wavelet shrinkage Granada iAstro Worshop

  13. The denoised KL basis Granada iAstro Worshop

  14. The residues and their analysis • Do not forget to denoise the mean ! • The reconstruction with the denoised KL is limited: • Not enough components • Adding components = increase the noise • The denoising can remove local significant feature • Use of the residues between the original data and the restored one Granada iAstro Worshop

  15. After the residue denoising Granada iAstro Worshop

  16. Spectra Sample Granada iAstro Worshop

  17. The velocity field Granada iAstro Worshop

  18. 3D visualisation Granada iAstro Worshop

  19. A spectrum in a cavity Granada iAstro Worshop

  20. A continuum image Granada iAstro Worshop

  21. The integrated continuum Granada iAstro Worshop

  22. CONCLUSION • Data cube can be denoised from KL • Limitation of the number of components • We could use more components with denoising • Too local information (spectral/spatial) • Residue denoising • Could be improved (best basis, softening rule, regularisation, ..) • Artifact removal • Use of ICA/SOBI blind source separation • Help for astrophysical interpretation Granada iAstro Worshop

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