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Blind Source Separation of Multispectral Astronomical Images

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1 Observatoire de la C te d'Azur (Nice) 2 Universit de Reims ... Mutual information, kurtosis. JADE (Cardoso et al.) based on the fourth order cumulant ... – PowerPoint PPT presentation

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Title: Blind Source Separation of Multispectral Astronomical Images


1
Blind Source Separation of Multispectral
Astronomical Images
  • Albert Bijaoui1 Danielle Nuzillard2
  • 1 Observatoire de la Côte d'Azur (Nice)
  • 2 Université de Reims Champagne Ardenne

2
Outline
  • Blind Source Separation (BSS) and images
  • BSS from Karhunen-Loève expansion
  • BSS from spatial correlations
  • BSS from independent component analysis
  • An experiment
  • HST/WFPC2 images of 3C120
  • Preparation
  • Results
  • Conclusions

3
Multispectral Astronomical Images
  • Today multispectral astronomical images
  • Well-defined spectral bands
  • Linear detectors
  • Space based observations
  • What information can be extracted?
  • Color indexes punctual sources
  • Color maps
  • Spectral models and parameters
  • Limits
  • Too many maps to draw
  • Images as mixtures

4
The Cocktail Party Model
  • The mixing hypotheses
  • Linearity
  • Stationarity
  • Source independence
  • The equation
  • Xi images - Sj unknown sources - Ni noise
  • aij mixing matrice

5
The Observations
  • WFPC2 HST Images of galaxy 3C120
  • F547M (V1) OIII Continuum (2x1100s)
  • F555W (V) F547MContinuum (2x1000s)
  • F675W (R) HaContinuum (2x1100s)
  • F814W (I) faint linesCont. (2x1100s)

6
The data set
  • Cosmic ray corrections
  • Extraction of the central part
  • 256x256 pixels 11  6x11  6
  • Variance stabilization
  • Generalized Anscombe transform
  • Background removal

7
The images after reduction
8
The Principal Component Analysis
  • Search of uncorrelated images
  • Signal as a statistical variable
  • The Principal Component Analysis
  • Linear combination with the greatest variance
  • Component subtraction and iteration
  • Eigenvectors and eigenvalues of the
    variance-covariance matrix
  • Astronomical applications

9
The Karhunen-Loève Expansion
  • PCA application to the images
  • Ergodicity
  • Autocorrelation best local representation
  • Cross-correlation decorrelation and energy
    concentration
  • Astrophysical applications
  • Data compression and denoising
  • Detection of faint variations
  • Classification
  • Energy spectrum

10
KLE of 3C120 images
11
KL expansion limitations
  • If Gaussian Probability Density Functions (PDF)
  • uncorrelated independent
  • If not
  • It may exist more independent sources than the
    ones resulting from the KL expansion
  • Orthogonality invariance by rotation
  • Two different approaches
  • To take into account the spatial correlations
  • To optimize an independent criterion

12
BSS from spatial correlations
  • SOBI (Belouchrani et al.)
  • Cross-correlations between sources and shifted
    sources
  • Number p of cross correlation matrices
  • Decomposition of the rotation matrix into
    n(n-1)/2 rotations between a couple of sources
  • Joint diagonalization
  • SOBI2 (Nuzillard)
  • Cross-correlations are made in the Fourier space
  • SOBI3
  • idem but adapted to 2D
  • SOBI4
  • 2D adaptation of SOBI1

13
Best visual Selection SOBI4-8
14
BSS from ICA
  • Contrast function
  • Mutual information, kurtosis
  • JADE (Cardoso et al.)
  • based on the fourth order cumulant
  • FastICA (Hyvärinen Oja)
  • Approximation of the negentropy
  • Different target functions
  • Fixed point algorithms

15
Best FastICA BSS
16
Interpretation of the source images
  • Source 1
  • The central galaxy region.
  • OIII lines play a role
  • Source 2
  • The ionized region surrounding the nucleus
  • OIII lines play a larger role
  • Source 3
  • Rings due to the PSF at the center for the Ha
    line
  • Source 4
  • Residue? Asymmetry
  • Source 1
  • The central galaxy region.
  • OIII lines play a role
  • Source 2
  • The ionized region surrounding the nucleus
  • OIII lines play a larger role
  • Source 3
  • Rings due to the PSF at the center for the Ha
    line
  • Source 4
  • Residue? Asymmetry

17
Source 3 and the PSF
  • Use of the TINY program

18
The resulting model
  • BSS leads to a simple two components model
  • A very bright nucleus which is not resolved in
    these exposures
  • A mainly gaseous region surrounding the galaxy
  • It is not a new model
  • We need more images for getting a more
    complicated one

19
Conclusions
  • The applied BSS methods were based on the
    cocktail party model.
  • Real multispectral astronomical images do not
    satisfy this model which requires
  • A linear combination of physical phenomena
  • A stationary mixing
  • A stationary white noise
  • They are typical tools for Data Mining
  • Adapted to hyperspectral observations
  • Adapted to analyze data from spectroimagers
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