Blind source separation from source separation to pixel classication
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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

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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


Blind source separation from source separation to pixel classication

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


Blind source separation from source separation to pixel classication

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

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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


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