HyperspectralRemoteSensing• Multi-spectral:Severalcomparativelywidespectralbands• Hyperspectral:Many(couldbehundreds)verynarrowspectralbands

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AVIRIS:AirborneVisible/InfraredImagingSpectrometer

• 224continuousspectralBands• 400-2500nm• Bandwitdth <10nm• Mainobjectiveistoidentify,

measure,andmonitorconstituentsoftheEarth'ssurfaceandatmospherebasedonmolecularabsorptionandparticlescatteringsignatures.

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Hyperion

• 220spectralchannels

• 357– 2576nm• 10nmbandwidth• 30-mresolution• 7.75kmswath• FliesonEO-1• 12-bitdynamicrange• LaunchedNov.20,

2000

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NextGeneration:HyperspectralInfraRed Imager(HyspIRI)https://hyspiri.jpl.nasa.gov

HyperspectralRemoteSensing• Doesnotlenditselftoconventionalimageviewingtechniques

withRGBcolorcomposites– Reducing>200bandsintothreedoesnottakeadvantageofthefull

spectrumofdata

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Radiancevs.Reflectance

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Thisistheaverageof25imagespectrameasuredbytheAVIRISsensoroverabrightdrylakebedsurfaceintheCuprite,Nevadascene.

Thespectralreflectancecurveforthesampleareaisactuallyrelativelyflatandfeatureless.

Thespectralreflectanceofthesurfacematerialsisonlyoneofthefactorsaffectingthesemeasuredvalues.

Radiancevs.Reflectance• Detectedradiancein

hyperspectral remotesensingisparticularlyaffectedby:– Solaremittance characteristicsas

afunctionofwavelength– Atmosphericconstituentsand

absorptionbands– Reflectancespectrumofsurface0

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Noatmosphere

CalibrationofHyperspectralData• Threemainconsiderationstakeninto

accountbeforetranslationofradiancevaluesintosurfacereflectances– Compensationforshapeofsolarspectrum

todetermineapparentreflectivity• Well-constrainedbymodels

– Compensationforatmosphericgastransmittanceandabsorptionbandswithintheatmospheretodeterminescaledreflectivity• Atmosphericradiative transfermodels

– Considerationoftopographiceffects• Digitalelevationmodels

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HyperspectralRemoteSensing• Challengesinusinghyperspectral data

– Datavolume• Multi-spectral:7-bands,8-bitdigitizationà 56elements• Hyperspectral220bands,12bitdigitizationà 2640

– Dataredundancy• Oftenthereislittledifferenceamongneighboringspectralbands• Thechallengeisfindingthosewithuniqueinformation• Redundantbandscanbeidentifiedusingthecorrelationmatrix

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ThecorrelationmatrixofnrandomvariablesX1,...,Xn isthen × n matrixwhosei,j entryisthecorrelationbetween(Xi), (Xj).

Ri, j =CVi, j

CVi,iCV j, j

CorrelationMatrix

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InsertFig.13.4

x1

x2

SpectralAngleMapperbasedClassification• InNdimensionalmultispectralspaceapixelvectorxhasbothmagnitude

(length)andananglemeasuredwithrespecttotheaxesthatdefinethecoordinatesystemofthespace.

• Forhyperspectral space,sometimestherearetoomanydimensionsandtheclassificationsbreakdown

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SpectralAngleMapperbasedClassification• Thespectralanglemappingapproachconsidersonlytheangular

information,reducingthedimensionalityoftheproblembynotconsideringthemagnitude

• Spectraarecharacterizedbytheiranglesfromthehorizontalaxes– Decisionboundariesaresetupfromlibraryinformationortrainingdata

definingsectorsfordifferentclasses– Spectraarelabeledaccordingtothesectorinwhichtheyfall– Requiresthatanglesaresufficientlydifferentfromoneanotherinorderto

defineclasses

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LibrarySearchingandSAM• SAMisappliedinmultidimensionalspacetocompareimagepixelspectrum

andalibraryreferencespectrum– themultidimensionalvectorsaredefinedforeachspectrumandtheangle

betweenthetwovectorsiscalculated.– Smalleranglesrepresentclosermatchestothereferencespectrum.– a“match”angularthresholdisappliedtodeterminewhetherornotapixelfallsin

aparticularangularclass

• SAMrepressestheinfluenceofshadingeffectstoaccentuatethetargetreflectancecharacteristics(DeCarvalhoetal.,2000)

• SAMisinvarianttounknownmultiplicativescalings,andconsequently,isinvarianttounknowndeviationsthatmayarisefromdifferentilluminationandangleorientation(Keshava,etal.,2002).

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ExpertSpectralKnowledgeandLibrarySearching

• Takesadvantageofthepresencesofdiagnosticallysignificantfeatures– Absorptionfeaturesthat

providetheinformationneededforidentification

– Requiressufficientspectralresolutionforthedistinction• Notjustidentifyingthedipsin

thereflectancebutalsoidentifyingtheshapesofthedips– Magnitude– Width:full-widthathalf

maximumdepth(FWHM)

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Spectralmixture• Mixed pixel: The signal detected by a sensor into a single pixel is

frequently a combination of numerous disparate signals.

• Mixed pixels are frequent in remotely sensed hyperspectral images due to insufficient spatial resolution of the imaging spectrometer, or due to intimate mixing effects.

• The rich spectral resolution available can be used to unmix hyperspectralpixels.

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Mixedpixel

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• The mixture problem can happen in macroscopic fashion, this means that a few macroscopic components and their associated abundances should be derived. • However, intimate mixtures happen at microscopic scales, thus complicating the analysis with nonlinear mixing effects.

LinearSpectralunmixing

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In linear spectral unmixing, the goal is to find a set of macroscopically pure spectral components (called endmembers) that can be used to unmix all other pixels in the data. • Unmixing amounts at finding the fractional coverage (abundance) of each endmember in each pixel of the scene, which can be approached as a geometrical problem:

LinearSpectralunmixing

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Physical constraints:• Abundances are non negative (non negativity constraint)• Abundances sum to one for each pixel (sum to one constraint)

SpectralUnmixing• M=thenumberofendmembers• N=thenumberofspectralbands• fm =thefractionofcoverageforaparticularclassm wherem

isfrom1toM• Rn istheobservedreflectanceinthenthspectralbandwhere

n isfrom1toN• an,m isthespectralreflectanceofthenth bandofthemth

endmember

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€

Rn = fman,m + ξnm=1

M

∑ n = 1, … N

Whereξn isanerrorinbandn

Observedreflectanceineachbandisthelinearsumofthereflectances oftheendmembers (withintheuncertaintyexpressedintheerrorterm)

SpectralUnmixing

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€

Rn = fman,m + ξnm=1

M

∑ n = 1, … N

Observedreflectanceineachbandisthelinearsumofthereflectances oftheendmembers (withintheuncertaintyexpressedintheerrorterm)

InMatrixform:R =Af +ξWheref isacolumnvectorofsizeM,Randξ arecolumnvectorsofsizeN,andAisanNx Mmatrixofendmember spectralsignaturesbycolumn

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R1Rn

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Spectralsignatureofclass1 Spectralsignatureofclassm

Reflectanceofapixelateachwavelength

Fractionofpixeloccupiedbyeachclass1- M

Errormatrix

SpectralUnmixing

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Fortheunmixing Matrix:R =Af +ξWetrytofindvaluesoff thatminimizeξIfweassumewehavethecorrectsetofendmembers,theequationsimplifiesto

R =AfWesolvethroughanerrorminimizationusingpsuedo inverse(Moore-Penrose)

f=(AtA)-1At RFormoreexplanationonthisminimizationreferto:

http://ltcconline.net/greenl/courses/203/MatrixOnVectors/leastSquares.htmForinformationonmatrixinversionsreferto:

https://ardoris.wordpress.com/2008/07/18/general-formula-for-the-inverse-of-a-3x3-matrix/

Solutionrequires:a)thesumofthefm valuesis1andb)0< fm < 1forallm

Summary:SpectralUnmixing• Mixedpixels:Apixelthatcontainsmultipleclasses• Oftenwewishtodistinguishsub-pixelinformation• Examples:

– IceandwaterinaMODISpixelorPassivemicrowavepixel– Mineralidentification– Sparsely-vegetatedareas– Diverselyvegetatedareas

• Mixedpixelproblemnotwelladdressedwithmultispectraldatabecausedistinctionswithlimitedbandnumberswerecleartodifferentiateclasses

• Withhyperspectral data,enoughofadistinctioncanbemadeformanysurfaceclasses

• Unmixing hasparticularrelevanceforsomethinglikemineralmappingwhereabundanceofmineralsisdesiredparameter

• Seekstodeterminethelinearcombinationofendmembers thatproducethespectralresponseofthepixel– Endmembers:purecovertypesthatarefoundinanimage

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