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Blind Source Separation : from source separation to pixel classication

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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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. Infomax (Bell & Sejnowski) • ANN output • Minimisation rule of the output entropy • Choice of the activation function • Natural gradient (Amari) iAstro / IDHA Worshop - Strasbourg Observatory

  9. 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

  10. 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

  11. The reduced HST images iAstro / IDHA Worshop - Strasbourg Observatory

  12. KL Expansion of 3C120 images iAstro / IDHA Worshop - Strasbourg Observatory

  13. Best visual Selection : f-SOBI iAstro / IDHA Worshop - Strasbourg Observatory

  14. 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

  15. FastICAsources after denoising iAstro / IDHA Worshop - Strasbourg Observatory

  16. Ground analysis iAstro / IDHA Worshop - Strasbourg Observatory

  17. 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

  18. 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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