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Tel: 043-290-3832
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URL: http://www.cr.chiba-u.jp/Newsletter No. 22
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$&.5*(k10 Y 45mV%wDz]r(1) Serreze, M. C., et al., 2007: Perspectives on the Arctic
shrinking sea-ice cover. Science, Vol.315, March 16,
p1533-1536.

(2) Naoki, K., et al., 2007: Thin sea-ice thickness as inferredfrom passive microwave and in-situ observations. JGR (tobe published)(3) Nishio, F., et al., 2007:

Physical and radiative

characteristics and long term variability of the Okhotsk
sea ice cover. JGR (to be published)(4) Comiso, J. & F. Nishio, 2007: Trends in the sea ice

cover using enhanced and compatible AMSR-E &SMMR. Data JGR (to be published)(5) Levitus, S., et al., 2000: Warming of the World Ocean.
Science,Vol.287, March 24, p2225-2229.

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Thomas Gathungu Ngigi I\QB[:IZ=[;> ¥ M Z J "ì Ä { Ù! §  Å Ò m pö  ³

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ðÆO7\VR   

Mix-unmix

äåºNKWBI

Classifier:

Under-determinedA

Models

Proposal
infor

Solving

Linear 

SpectralU?O1EIo£  Unmixing‘…the number of bands must be more than the  ­b`t"    ª  ©þ ©" 2

number of end-members…’ is perhaps the mostA2".©¬#aòvq#{Ùubiquitous statement in linear spectral unmixing. Most"G\Q#ðÆO7\VR0conventional linear spectral unmixing techniques fix theðl

number of end-members on the dimensionality of the#O7\VR"CZD\#U?O1
WS\ICZ@Z

data, and none of them can derive multiple (2+)=úÁâ¦".ò£Ø[ÉÌa·

end-members from a single band. The Mix-unmixäåº0

Classifier overcomes the two limitations.

EIo£/

ÁÃ

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environment that allows any pixel to be unmixed withoutMix-unmix

Classifier

creates

aprocessing5

any sort of restrictions (e.g. minimum determinablefraction), impracticalities (e.g. negative fractions), ortrade-offs (e.g. either positivity or unity sum) that may be

associated with conventional unmixing techniques.
The Mix-unmix Classifier gives not only the mostprobableDN(digitalnumber)contributions

ofend-members but also, unlike conventional unmixing
techniques, their most probable contributory DNs. The
contributory DNs directly define for instance thephenological stages of the end-members.
Theory of the classifier: As the term implies, theMix-unmix Classifier consists of two branches, namely
mixing and unming. The mixing branch entails
development of a hypothetical mixed end-members
image from the desired end-members’ spectra by linearlymixing the spectra at all possible percentages (dependingon the mixture interval adopted) and in all possible DN
combinations (depending on the ranges of the spectra).
Unmixing involves determination of each real (raw)image pixel DN’s contributory end-members and theirpercentages by back propagating through the mixing
branch using a pixel of the same DN in the hypotheticalimage as a proxy.
As the mixture model is truly never known, in case areference training image exists, the Mix-unmix Classifier
after initially linearly unmixing a raw image, normalises
the linearly-estimated percentages based on reference
training percentages.
Preliminary studies show that the Mix-unmix
Classifier performs better than; Spectral Angle Mapper,
Binary Encoding classifier, and Maximum Likelihoodclassifier (hard classifiers), and IDRISI Kilimanjaro
Probability Guided Option linear spectral unmixingtechnique.
2007 . 9 6 28 5Thomas Gathungu NgigiG1

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