21/22 February 2003Granada iAstro Worshop1 Analysis of Astrophysical Data Cubes using...

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

21/22 February 2003


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

21/22 February 2003


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

21/22 February 2003


BEAR : an IFTS device

21/22 February 2003


BEAR at the CFHT focus

21/22 February 2003


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

21/22 February 2003


The data cube

21/22 February 2003


Spectra sample

21/22 February 2003


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)

21/22 February 2003


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

21/22 February 2003


The noisy KL basis

21/22 February 2003


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

21/22 February 2003


The denoised KL basis

21/22 February 2003


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

21/22 February 2003


After the residue

denoising

21/22 February 2003


Spectra Sample

21/22 February 2003


The velocity

field

21/22 February 2003


3D visualisation

21/22 February 2003


A spectrum in a cavity

21/22 February 2003


A continuum image

21/22 February 2003


The integrated continuum

21/22 February 2003


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

21/22 February 2003Granada iAstro Worshop1 Analysis of Astrophysical Data Cubes using...

Documents

Transcript of 21/22 February 2003Granada iAstro Worshop1 Analysis of Astrophysical Data Cubes using...