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Binarytomographicimagereconstruction000
Figure104:Imagesreconstructedfromnoise-freedatawithAlgorithm3fork1100,
Kc140,T010.5:(upperrow)∆V
j
(GR)
(δ10.01):;10.05(left),
;10.1(middle),
;10.3(right);(bottomrow)∆V
j
(BS)
,;10.05:p11.5(left),p11.1(middle),p11.9
(right)
NoiseRatio(SNR)thatiscomputedaccordingtothedefinition:
SNRś20log
||˜
bexact||2
||n||2
[dB],
(1.51)
where˜
bandnaregivenby(1.2).WehaveusedthenoisydataforwhichSNR1
20dB.
SomeresultsobtainedwithAlgorithms2,3,andtheMulti-DiscreteAlgorithm
(MDA)givenby(1.42)havebeenpresentedin[67,70],andtheywillnotbedis-
cussedhere.ThenewresultsthatareobtainedwithAlgorithm3,andAlgorithm
4,areshowninFigs.1.4–1.7,andinFigs.1.8–1.10,respectively.Algorithm3
hasbeenrunwithdifferentcliqueenergyfunctions(V
j
(HL)
,V
j
(GR)
,andV
j
(BS)
),and
theassociatedparameters(;,δ,andp),butwepresenttheresultsonlyforthe
V
j
(GR)
andV
j
(BS)
.TheresultsobtainedforV
j
(HL)
areslightlyworsethanforV
j
(GR)
.
InAlgorithm4,weappliedonlytheGaussianpriorsinceonlyforthiscasethe
computationalcostisverylow.
TheparametersT0andKcwhichsetthetemperatureschedulearenearlythe
sameasin[70].Theyareadjustedoptimally,butingeneral,highervaluesofthe
parametersalwaysimprovethequalityofthereconstructionbutatthecostofa
convergencerate.
ThescalingparameterδinV
j
(HL)
andV
j
(GR)
isestimatedusingtheMaximum
