Abstract

In this work, an alternative route to analyze a set of coherency matrices associated to a medium is addressed by means of the Independent Component Analysis (ICA) technique. We highlight the possibility of extracting an underlying structure of the medium in relation to a model of constituent components. The medium is considered as a mixture of unknown constituent components weighted by unknown but statistically independent random coefficients of thickness. The ICA technique can determine the number of components necessary to characterize a set of sample of the medium. An estimate of the value of these components and their respective weights is also determined. Analysis of random matrices generated by multiplying random diattenuators and depolarizers is presented to illustrate the proposed approach and demonstrate its capabilities.

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References

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2010 (2)

2009 (1)

2007 (3)

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40(1), 1–47 (2007), doi:.
[CrossRef]

R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. 32(6), 689–691 (2007).
[CrossRef] [PubMed]

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, “Geometric means in a novel vector space structure on symmetric positive-definite matrices,” SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007).
[CrossRef]

2004 (1)

2000 (1)

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4-5), 411–430 (2000).
[CrossRef] [PubMed]

1999 (1)

A. Hyvärinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Trans. Neural Netw. 10(3), 626–634 (1999).
[CrossRef] [PubMed]

1996 (2)

1987 (1)

1986 (1)

S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttg.) 75, 26–36 (1986).

1978 (1)

1948 (1)

Arsigny, V.

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, “Geometric means in a novel vector space structure on symmetric positive-definite matrices,” SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007).
[CrossRef]

Ayache, N.

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, “Geometric means in a novel vector space structure on symmetric positive-definite matrices,” SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007).
[CrossRef]

Azzam, R. M. A.

Barakat, R.

Borghi, R.

Chipman, R. A.

Cloude, S. R.

S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttg.) 75, 26–36 (1986).

De Martino, A.

Devlaminck, V.

Fillard, P.

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, “Geometric means in a novel vector space structure on symmetric positive-definite matrices,” SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007).
[CrossRef]

Gil, J. J.

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40(1), 1–47 (2007), doi:.
[CrossRef]

Gori, F.

Goudail, F.

Guyot, S.

Hyvärinen, A.

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4-5), 411–430 (2000).
[CrossRef] [PubMed]

A. Hyvärinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Trans. Neural Netw. 10(3), 626–634 (1999).
[CrossRef] [PubMed]

Jones, R. C.

Kim, K.

Lu, S. Y.

Mandel, L.

Morio, J.

Mukunda, N.

Oja, E.

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4-5), 411–430 (2000).
[CrossRef] [PubMed]

Ossikovski, R.

Pennec, X.

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, “Geometric means in a novel vector space structure on symmetric positive-definite matrices,” SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007).
[CrossRef]

Santarsiero, M.

Simon, B. N.

Simon, R.

Simon, S.

Wolf, E.

Eur. Phys. J. Appl. Phys. (1)

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40(1), 1–47 (2007), doi:.
[CrossRef]

IEEE Trans. Neural Netw. (1)

A. Hyvärinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Trans. Neural Netw. 10(3), 626–634 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

Neural Netw. (1)

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4-5), 411–430 (2000).
[CrossRef] [PubMed]

Opt. Lett. (2)

Optik (Stuttg.) (1)

S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttg.) 75, 26–36 (1986).

SIAM J. Matrix Anal. Appl. (1)

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, “Geometric means in a novel vector space structure on symmetric positive-definite matrices,” SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007).
[CrossRef]

Other (1)

A. Aiello and J. P. Woerdman, arXiv.org e-print archive math-ph/0412061 (2004)

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Tables (3)

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Table 1 Examples of Generated Mueller Matrices. First Column: MD Values, Second Column: MDEP Values, Third Column: M= MD MDEP

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Table 2 Estimated Mean Mueller Matrix. First Column: Mmean, Second Column: MD Values, Third Column: MDEP Values

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Table 3 Estimated Mc Mueller Matrix Associated to Each Component. First Column: Mc(i), Second Column: MD(i) Values, Third Column: MDEP(i) Values

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

H= ij m ij ( σ i σ j * )
dM( z ) dz =m M( z )
H 1 H 2 =exp[ Log( H 1 )+Log( H 2 ) ]
( αH )=exp[ α Log( H ) ]
H=( α 1 G 1 )( α 2 G 2 )( α N G N )=exp[ i=1 N α i Log( G i ) ]
LH= log(H) = j=1 N α j D j
D j =[ d 1 j d 5 j +i d 6 j d 7 j +i d 8 j d 9 j +i d 10 j . d 2 j d 11 j +i d 12 j d 13 j +i d 14 j . . d 3 j d 15 j +i d 16 j . . . d 4 j ]
X=A( S S )+ X
H LE = exp( 1 K j=1 K log( H j ) )
M DEP =[ 1 p q r 0 a 0 0 0 0 b 0 0 0 0 c ]
H i = exp[ α i D i +log( H LE ) ]
X- X =A S 1
S= S 1 +W X or S 1 = SW X
S 1 = WX-W X
S = W X

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