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Blind Source Separation : from source separation to pixel classication. Albert Bijaoui 1 , Danielle Nuzillard 2 & Frédéric Falzon 3 1 Observatoire de la Côte d'Azur (Nice) 2 Université de Reims Champagne Ardenne 3 Alcatel Space – Cannes-la-Bocca. O utlines.

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blind source separation from source separation to pixel classication

Blind Source Separation : from source separation to pixel classication

Albert Bijaoui1, Danielle Nuzillard2

& Frédéric Falzon3

1 Observatoire de la Côte d'Azur (Nice)

2 Université de Reims Champagne Ardenne

3 Alcatel Space – Cannes-la-Bocca

iAstro / IDHA Worshop - Strasbourg Observatory

o utlines
Outlines
  • What is Blind Source Separation (BSS)?
  • Different BSS tools
    • Karhunen-Loève expansion (KL/PCA)
    • Independent Component Analysis (ICA)
    • Use of spatial correlations (SOBI, ..)
  • Experiment on HST/WFPC2 images
    • Source separation
  • Experiment on Multispectral Earth images
    • Pixel classification
  • Conclusion

iAstro / IDHA Worshop - Strasbourg Observatory

the cocktail party model
The Cocktail Party Model
  • The mixing hypotheses
    • Linearity
    • Stationarity
    • Source independence
  • The equation:
  • Xiimages - Sjunknown sources - Ninoise
  • A= [aij]mixing matrix

iAstro / IDHA Worshop - Strasbourg Observatory

kl and pca
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
  • KL 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

iAstro / IDHA Worshop - Strasbourg Observatory

mutual information
Mutual Information
  • Mutual Information between l variables
  • Case of Gaussian distributions
    • R is the matrix of correlation coefficients
    • In this case : Uncorrelated = Independent

iAstro / IDHA Worshop - Strasbourg Observatory

independent component analysis
Independent Component Analysis
  • Contrast Function :
    • Mutual information of the sources
  • Contrast:
  • Minimum Mutual information = Maximum contrast
  • How to compute the source entropy ?

iAstro / IDHA Worshop - Strasbourg Observatory

slide7
JADE
  • Comon’s approach
    • PDF Edgeworth Approximation
    • Cumulants use
  • JADE (Cardoso & Souloumiac)
    • Based on order 4 cumulants
    • Rotation of KL separation matrix
    • Jacobi decomposition (2 à 2)
    • Joint Diagonalisation

iAstro / IDHA Worshop - Strasbourg Observatory

infomax bell sejnowski
Infomax (Bell & Sejnowski)
  • ANN output
  • Minimisation rule of the output entropy
  • Choice of the activation function
  • Natural gradient (Amari)

iAstro / IDHA Worshop - Strasbourg Observatory

fastica
FastICA
  • Helsinki : Oja, Karhunen, Hyvärinen
  • Negentropy
    • Negentropy = Entropy Gaussian rv – Entropy rv
  • Negentropy approximation
  • Choice of the function G
    • Cumulant order 4, Sigmoid, Gaussian

iAstro / IDHA Worshop - Strasbourg Observatory

bss from spatial correlations
BSS from spatial correlations
  • SOBI (Belouchrani et al.)
    • Cross-correlations between sources and shifted sources
    • Number p of cross correlation matrices
    • Jacobi / Givens decomposition
    • Joint diagonalization
  • F-SOBI (Nuzillard)
    • Cross-correlations are made in the Fourier space

iAstro / IDHA Worshop - Strasbourg Observatory

the reduced hst images
The reduced HST images

iAstro / IDHA Worshop - Strasbourg Observatory

kl expansion of 3c120 images
KL Expansion of 3C120 images

iAstro / IDHA Worshop - Strasbourg Observatory

best visual selection f sobi
Best visual Selection : f-SOBI

iAstro / IDHA Worshop - Strasbourg Observatory

slide14

CASIImages 9 filters394-907nmImages from GSTB (Groupement Scientifique de Télédétection de Bretagne) with the courtesy of the Pr. Kacem Chehdi ENSSAT Lannion (France)

iAstro / IDHA Worshop - Strasbourg Observatory

fastica sources after denoising
FastICAsources after denoising

iAstro / IDHA Worshop - Strasbourg Observatory

ground analysis
Ground analysis

iAstro / IDHA Worshop - Strasbourg Observatory

classification
Classification
  • A source is not a pure element
  • Pixel classification is easily deduced by comparison to the ground analysis
  • BSS allows one to facilitate classification
  • New classes are probed by BSS analysis

iAstro / IDHA Worshop - Strasbourg Observatory

conclusion
Conclusion
  • Used BSS methods were based on the cocktail party model.
  • Typical tools for Data Mining
  • Adapted to multi-wavelengths observationsor data from spectroimagers
  • Many applications : source identification, pixel classification, denoising, compression, ..

iAstro / IDHA Worshop - Strasbourg Observatory