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2.Numericalproblemanalysis
ofcomplexgeometry,wherethemediummayshowfeaturesoftheinhomogeneity
ofcurrents,conductivity,etc.Mostofthecurrentlyusedimagereconstructionalgo-
rithmsusethismethod.Dependingonthegeometryofthearea,thereisatendency
touseisoparametricfiniteelementsoftriangularorquadrangular.
Thefoundationofmostofthecurrentlyusedimagereconstructionalgorithmsin
theEITistheequation:
(2.1)
withtheboundaryconditionsofDirichlet(2.2)andNeuman(2.3):
(2.2)
(2.3)
Substitutingequation(2.1)relationship
(2.4)
and
(2.5)
arelationshipbetweenthepotentialdistributionu,andtheconductivitydistribution
γinthestudyarea:
(2.6)
Theequation(2.6)alongwiththeboundaryconditions(2.2)and(2.3)iscalledthe
forwardfieldproblem.Thesolutionofthisequationleadstothedeterminationof
thedistributionofthestatefunctionintheconsideredarea.Supposeavectoruis
avectorofthepotentialsmeasuredattheedgeofthearea,whereasγarethepa-
rameterswithinanarea(distributionofconductivity).Thesevectorsareboundto
acertain,non-linearTtransformation.Thematrixofthistransformationdetermines
thesolutionoftheLaplaceequation:
(2.7)
Withtheaboveassumptions,thetaskoftheEITistodeterminetheinversetransfor-
mationtotheTtransformationthatwouldmapthevectorumtothevectorγ:
(2.8)
Theequation(2.8)isalsocalledtheinversefieldproblem.Ingeneral,thesize
ofthevectorumisatleastequaltothesizeofthevectorγ,hencethesolutiontothis
problemisnotstraightforward.
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