Blind Source Separation : from source separation to pixel classication - PowerPoint PPT Presentation

Loading...

PPT – Blind Source Separation : from source separation to pixel classication PowerPoint presentation | free to view - id: 13dfbf-ZTNjY



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Blind Source Separation : from source separation to pixel classication

Description:

1 Observatoire de la C te d'Azur (Nice) 2 Universit de Reims Champagne Ardenne. 3 Alcatel Space Cannes-la-Bocca. 28 November 2002 ... – PowerPoint PPT presentation

Number of Views:227
Avg rating:3.0/5.0
Slides: 19
Provided by: albertb2
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Blind Source Separation : from source separation to pixel classication


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

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

3
The Cocktail Party Model
  • The mixing hypotheses
  • Linearity
  • Stationarity
  • Source independence
  • The equation
  • Xi images - Sj unknown sources - Ni noise
  • A aij mixing matrix

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

5
Mutual Information
  • Mutual Information between l variables
  • Case of Gaussian distributions
  • R is the matrix of correlation coefficients
  • In this case Uncorrelated Independent

6
Independent Component Analysis
  • Contrast Function
  • Mutual information of the sources
  • Contrast
  • Minimum Mutual information Maximum contrast
  • How to compute the source entropy ?

7
JADE
  • Comons 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

8
Infomax (Bell Sejnowski)
  • ANN output
  • Minimisation rule of the output entropy
  • Choice of the activation function
  • Natural gradient (Amari)

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

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

11
The reduced HST images
12
KL Expansion of 3C120 images
13
Best visual Selection f-SOBI
14
CASI Images 9 filters 394-907nm Images from
GSTB (Groupement Scientifique de Télédétection de
Bretagne) with the courtesy of the Pr. Kacem
Chehdi ENSSAT Lannion (France)
15
FastICA sources after denoising
16
Ground analysis
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

18
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, ..
About PowerShow.com