SPECT( Single Photon Emission CT )

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SPECT( Single Photon Emission CT ) PET( Positron
Emission CT ) ??? ????????? ??????????
FBP ( Filtered Back Projection ) ????????
Iterative Reconstruction MLEM ( Maximun
Likelihood Expectation Maximization ) OSEM (
Ordered Subsets Expectation Maximization )
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Convolution ????
FBP Filtered Back Projection
( )
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SimpleBackProjection???SPECT?????
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?????????????1?????? 32??????????????????? ??????
???????????????? 2??????( P? )??????
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??????????? Simple Back Projection ??????????????
2??????( P? )? ??????????????????? (??????????????
????????) ????j??????????????? ?????????????1????
?? 32??????????????????? ?????????????1??????? ??
????????????2??????P??????? P??????????????l????
l? P? d? (Simple back projection) l
????????????????????? ???????????????????????
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123I-IMP Brain SPECT ???????????????????????????
???????
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?????????????r????????????? ???? 1/r
???????g???????? l ???? ??????? lg(1/r)
???? l?g?1/r ???????? L?G?F(1/r)
? ??????????????? LGF(1/r) ???? 2?????????????
?????????? (fr??????????????? ) F(1/r)
??(1/r)exp(-j(2prfr ))rdrd? 1/fr ????
GfrL
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?????? Convolution
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??????? ??? g ?????????? ????????? G ? ?????
Ramp???? H ???? ??????????? ???????? Ramp???? h
? g ????????????????? ( G x H ? g h ????? )
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convolution.c ????? ??????????? g ? ????
Ramp???? ? ?????
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???? Convolution l g h ??????? g ?
???Ramp???? h ????????? l ??????
//--------- Convolution h into g
--------------- for( i1 ilt256 i )
gh 0.0 for(j0 jlt127 j) if(
ij lt 256) gh g ij h j
for(j1 jlt127 j) if( i-j gt 1 ) gh g
i-j h j li gh
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??? Ramp???? h ? ???? 1 ???? ??????? g ? l(
gh) ????????
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?????? Ramp???? ? ???
convolution_FFT.c ?????
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??? g ?????? Gr?Gi ?? ????? Ramp???? H
? ??????????????? ???????? Ramp???? h ? g
?????????????? ??? ( G x H ? g h ????? )
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?????2??????P? (????????)?????????? l
???????L??????? fr ???????( fr L
)?????????????????? g ???? ??????????????????? ??
?????????????????? P? ? ??????? h (
fr???????? ) ??????? ???????????? g ???2??????
P? ? ?????? ?????????????????????? H(
fr)? ????????(???)? ????????????????????????????
????????????
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?????????????? H?? H fr(fr??????????????) H
0 (fr??????????????) ???? ???Ramp????????
Ramp?????????????? ???Ramp????h?????? ????P??h??
????
P? P? h ( ??????? )
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h??????2?????? P? ???????????? g ?? g ? P? d?
( Filtered back projection ) Filtered back
projection ?? ?????????????????????? ????h????????
?????????????
h??????2?????? P? ???????????? g ? P? d? (
Filtered back projection )????????????????????????
????h?????????????????????
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Ramp??????????????????????? ??????????????
?????????????? ????????????????????????
??? ??????????????????? ??????????????????????????
?? ???????? SPECT????????????????????? SheppLogan
???????? ????????????????????????? ???????????????
???? ??????????????????????????? ??????????
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????????????2??????(P?)? ???????
???????????????? ????????????????????????
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??????? 64x64??? Shepp Logan ????
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????????????? Shepp Logan???????????????? 1
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MIBI ??SPECT???? ??????????? ???? 99mTc-MIBI
?????????? ?????(99mTc-MIBI ???????)? ??????RI???
???????? ???????????????????????? ?????????????
(99mTc-MIBI??????????(????????)????)
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123I-IMP Brain SPECT FBP with Ramp
filter
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123I-IMP Brain SPECT FBP with SheppLogan filter
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?????? 18F-FDG ?PET ??????
?PET????????????????? ?????????
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?PET???????? Ramp????? ????????? FBP??
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????? ?????? ? yi yj ????? µ i j
4?????? ????????
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?????µ???? 128 10 ???? ?????? ? yi yj
?????(????)
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?????µ???? 128 128 ???? ?????? ? yi yj
?????(????)
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?????µ???? i j ???? ??????? yi yj
?????(????)?? 4???? C i j yi yj
???? ?SC µ ?????? S(???? x ?????)
???????? ? yi yj SS C i j yi
yj µk i j µk i j ??k
?????????????
i j
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?????????? ? ? ????? µ (???? ????1) ???? ?/(S C
µ) ????? ?/(S C µ) ???????? /
??µ????????????? ????µ????????????????? ?/(S C
µ) ? 1 ?? ???? ????µ????????????????? ?/(S C µ)
? 1 ?? ????
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S C (?/(S C µ)) / SC ??????????? ?/(S C µ)
??? (???? C ????????)????? ???????? SS
Cijyiyj (?yiyj/(SSCijyiyj µk
i j )) / SSCijyiyj
????????( ???? i x j )
i j
yi y j
yi y j
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k ????????µk ? ?????? S C (?/(S C µ)) / SC
????????????? µk1 ???????? µk1 /µk S C (?/(S
C µ)) / SC ???????? MLEM?OSEM ??
???????? µk1 i j /µk i j
SS Cijyiyj (?yiyj/(SSCijyiyj
µk i j )) / SSCijyiyj

i j
yi y j
yi y j
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OSEM ?? yj (???????????)?????? ????? C (?/(S C
µ)) / SC ????????????? µ???????? ???? yj ? 0,
1, 2, 3, 4, 5, 6, 7, 8 ? 9???? subsets ? 3
??????? ???yj 0, 3, 6 ??? µk ?????? ???yj 1,
4, 7 ??? µk ??? µk1 ?????? ???yj 2, 5, 8 ???
µk1??? µk2 ?????? ???? MLEM ?
1??????????? MLEM ? 3????????????????????
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//------------------------------------------------
------------------------------- // OSEM
//---------------------------------------------
---------------------------------- for(k0klt20k
) for(sub0 sublt8 sub) s1 sub -
2(int)((double)sub/2.0) s2 1-s1
for(j0jlt192j) for(i0ilt192i)
S_YC_CMij SCij 0.0
for(j0jlt192j) printf("\n j d ", j)
for(i0ilt192i) for(yjsub yjlt32
yj8) for(yiCZLjiyj0
yiltCZLjiyj1yi) CM0.0
for(jj0jjlt192jj) for(iiCZMyjyijj0i
iltCZMyjyijj1ii)
CM
Ciijjyiyj Miijjks1
S_YC_CMij Yiyiyj Cijyiyj /
CM SCij Cijyiyj //
yi, yj // i, j
for(j0jlt192j) for(i0ilt192i)
if(SCijgt0.) Mijks2
Mijks1 S_YC_CMij / SCij
// j, i // sub
for(j0jlt192j) for(i0ilt192i)
Mijk1s2 Mijks2 // j, i
Disp_M(k,s2) printf("\n\nNext iteration ?
")scanf("c",yn) if(yn'n')break // k
OSEM ????? ????????????? for???
????????????????
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OSEM ????
Subsets 2 ???????? k k 0 k 2
k 4 k 10 k 20
?????? ( ???????????????? ) ????????????
?????????
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?????µ??????????????? ? ?????? C ?????????
??????????
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???? C ???? ????????????? ????????
??????? ??????? ? ??????? ?????????????????? PVC
( Partial Volume Correction ) ???? C ? ?????
???? ???
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MRP (Median Root Prior)????? ???(Bayes)?????????
?? ??????????(???? Prior )????? µk1/µk
SC(?/(SCµ))/ (SC Prior ) Prior ?????????µk ?
???????? M (median)??? ????????µk1
?????? Median Root Prior ß ( µk ? M ) / M
M ??????(3x3????)???? (median)? ß?????????
????? ( 0 lt ßlt 1 )? ( ß ? 0 ???? OSEM ??? )
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MRP 18F-FDG ?PET M matrix size 3 x 3 x
3
MRP ???? ?? ?????????? ???????????
????????????????????
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MRP??ß?????????????????COV ???????????????????
Alenius S, Ruotsalainen U. Eur J Nucl
Med (1997) 24
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MRP????????????????????????? (????????)?
Alenius S, Ruotsalainen U. Eur J Nucl
Med (1997) 24
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???????? ?????????? ??????? Prior ??? ????
C ??? ????????????????????
????????????????? ?????? C ????? ????????????