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21/22 February 2003
Granada iAstro Worshop 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
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21/22 February 2003
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
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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
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Granada iAstro Worshop 4
BEAR : an IFTS device
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21/22 February 2003
Granada iAstro Worshop 5
BEAR at the CFHT focus
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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
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21/22 February 2003
Granada iAstro Worshop 7
The data cube
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21/22 February 2003
Granada iAstro Worshop 8
Spectra sample
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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)
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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
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Granada iAstro Worshop 11
The noisy KL basis
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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
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Granada iAstro Worshop 13
The denoised KL basis
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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
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Granada iAstro Worshop 15
After the residue
denoising
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21/22 February 2003
Granada iAstro Worshop 16
Spectra Sample
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Granada iAstro Worshop 17
The velocity
field
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Granada iAstro Worshop 18
3D visualisation
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Granada iAstro Worshop 19
A spectrum in a cavity
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Granada iAstro Worshop 20
A continuum image
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Granada iAstro Worshop 21
The integrated continuum
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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