Blind Source Separation : from source separation to pixel classication

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28 November 200 2 iAstro / IDHA Worshop - Strasbourg O bservatory 1 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

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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. - PowerPoint PPT Presentation

Transcript of Blind Source Separation : from source separation to pixel classication

Page 1: Blind Source Separation :  from source separation  to pixel classication

28 November 2002

iAstro / IDHA Worshop - Strasbourg Observatory

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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

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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

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iAstro / IDHA Worshop - Strasbourg Observatory

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The Cocktail Party Model• The mixing hypotheses

– Linearity– Stationarity– Source independence

• The equation:

ijj iji NSaX • Xi images - Sj unknown sources - Ni noise

• A= [aij] mixing matrix

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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

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iAstro / IDHA Worshop - Strasbourg Observatory

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Mutual Information

• Mutual Information between l variables

• Case of Gaussian distributions

– R is the matrix of correlation coefficients– In this case : Uncorrelated = Independent

li

i

ll

nn

ln

s

nnpnnpSSIp

i

l

,1

121

,...,

1)(),...,(log),...,(),...,(

1

RI detlog21

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Independent Component Analysis• Contrast Function :

– Mutual information of the sources

• Contrast:

• Minimum Mutual information = Maximum contrast

• How to compute the source entropy ?

AXXESESSI n

l

ll detlog),...,()(),...,( 211

ASESSCl

ll detlog)(),...,( 21

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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

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Infomax (Bell & Sejnowski)

• ANN output

• Minimisation rule of the output entropy

• Choice of the activation function

• Natural gradient (Amari)

)(XY g

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FastICA• Helsinki : Oja, Karhunen, Hyvärinen

• Negentropy– Negentropy = Entropy Gaussian rv – Entropy rv

• Negentropy approximation

• Choice of the function G- Cumulant order 4, Sigmoid, Gaussian

pyG GEyGEyJ )()()(

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iAstro / IDHA Worshop - Strasbourg Observatory

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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

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The reduced HST images

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KL Expansion of 3C120 images

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Best visual Selection : f-SOBI

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CASIImages 9 filters

394-907nmImages from GSTB (Groupement Scientifique

de Télédétection de Bretagne) with the courtesy of the Pr. Kacem Chehdi ENSSAT

Lannion (France)

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FastICAsources

after denoising

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Ground analysis

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iAstro / IDHA Worshop - Strasbourg Observatory

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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

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Conclusion

• Used BSS methods were based on the cocktail party model.

• Typical tools for Data Mining

• Adapted to multi-wavelengths observations or data from spectroimagers

• Many applications : source identification, pixel classification, denoising, compression, ..