????(CT,SPECT,PET)???????????

1
(No Transcript)
2
(No Transcript)
3
(No Transcript)
4
????(CT,SPECT,PET)??????????? 2????? Pre-filter
??????? ????????????????????????
Butterworth, Wiener ???? ??? Reconstruction
filter ??????? FBP(??????????)????????
????????????(?????)??? ????????????????????
Ramp?SheppLogan ?Chesler? Ramachandran ???????
5
???????????????? ????????????????? ?????????????
?????????? 3?????C?????????? ???????????????????
(????????)
6
??? ????????? FFT.c
7
?????? (Fourier Transform)??????? ??????????(?????
)???????? ????(??)????????????????? 50Hz?????????
????????????
???? 1????????
???????
50Hz?????????(Hum)
8
(No Transcript)
9
?????? (Fourier Transform)?????? ??????
??????????????????
10
???????? ( FFT Fast Fourier Transform
) ????????????????????? 1942?? Danielson ?
Lanczos ???? ????????????????????????? ??????????
? e(2pf t )i ????W nk ??? ??????????? ?????????(
IFFT Inverse FFT )? ????????????????????????????
FFT ? IFFT ??????????????? ????? 2?????????????
11
2?? FFT ?????? 2??????? ?????4???? ( 0,0 )(
????)? ??????????????? ????????????? 1/4 ????????
12
??? img ? x ????2?? FFT ????? 2????????sin???
x ??cos??? y ??????? x ? y ??4???? (
0,0 ) ?????? ??? 2????????? ( IFFT )
???? ??????x ? ?????????????
13
Butterworth.c ?????? ???????? ?? ?????? ????
14
????????????????????? ?????????? Butterworth
filter ?????????????????????
15
1??? Butterworth filter ? 2???????? 2????????sin?
? x ?cos?? y ? 4???? ( 0,0 ) (
????)??????? 4????????????? ??????2???
Butterworth filter B2 ??x ?y
?4??????????????
16
Original Image Frequency spectrum
Frequency space filtering
FFT
Filtered Frequency spectrum
Filtered Image
IFFT
17
Convolution ????
FBP Filtered Back Projection
( )
18
SimpleBackProjection???SPECT????? SimpleBackProjec
tion.c ????
19
Reconstruction position j ?0??63???????? (????????
??????????????) ????????23?????????????????? ???
?????????????????? ????????????????????
20
?????????????1?????? 32??????????????????? ??????
???????????????? 2??????( P? )??????
21
??????????? Simple Back Projection ??????????????
2??????( P? )? ??????????????????? (??????????????
????????) ????j??????????????? ?????????????1????
?? 32??????????????????? ?????????????1??????? ??
????????????2??????P??????? P??????????????l????
l? P? d? (Simple back projection) l
????????????????????? ???????????????????????
22
(No Transcript)
23
123I-IMP Brain SPECT ???????????????????????????
???????
24
?????????????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 ????
L G /fr ??? GLfr
25
G Lfr ? ???? 2?????????? ??????????????????2???
?? L ?? ?????? fr( fr???????????????) ????????????
?????????????? G ???? GLfr ?????????
? ??????????????????? ?????? ????
??????????? glh ( h ? ????fr ? ??????? )
( ??????? )
26
?????l? P? d? ??????? g ? P? d? h (
??????? ) g ?( P? h)d? (h??????????????) g ?
P? d? ( P? P? h ) FBP?? P? ? ??????? h (
fr???????? ) ??????? ???????????? g ???2??????
P? ? ?????? ??? Filtered Back Projection (FBP)
???? ?????????????????????? H(
fr)? ????????(???)? ????????????????????????????
????????????
27
?????????????? H?? H fr(fr??????????????) H
0 (fr??????????????) ???? ???Ramp????????
Ramp?????????????? ???Ramp????h?????? ????P??h??
????
P
P? P? h ( ??????? )
28
????????????? Filtered Back Projection
(FBP) ???????2?????? P? ? ? ??????? h (
fr???????? ) ??????? ???????????? g ???2??????
P? ? ??????
29
??????? ??? g ?????????? ????????? G ? ?????
Ramp???? H ???? ??????????? ???????? Ramp???? h
? g ????????????????? ( G x H ? g h ?????
) ( G ?? g ??????? ) ( H ???? h
??????? )
30
?????? Convolution
31
(No Transcript)
32
(No Transcript)
33
convolution.c ????? ??????????? g ? ????
Ramp???? ? ?????
34
???? 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
35
?????? Ramp???? ? ???
convolution_FFT.c ?????
36
??? g ?????? Gr?Gi ?? ????? Ramp???? H
? ??????????????? ???????? Ramp???? h ? g
?????????????? ??? ( G x H ? g h ????? )
37
h??????2?????? P? ????????????g ?? g ? P? d?
( Filtered back projection ) Filtered back
projection ?? ?????????????????????? ????h????????
?????????????
h??????2?????? P? ???????????? g ? P? d? (
Filtered back projection )????????????????????????
????h?????????????????????
38
Ramp??????????????????????? ??????????????
??????????????????????????????????????
?????????????????????? ???????????????????????????
????????? SPECT????????????????????? SheppLogan??
?????? ???????????????????????????????????????????
? ?????????????????????????????????????
39
????????????2??????(P?)? ???????
???????????????? ????????????????????????
40
??????? 64x64??? Shepp Logan ????
41
????????????? Shepp Logan???????????????? 1
42
???????( position j )? 37 ??????? ???? 99mTc-MIBI
?????????? ?????(99mTc-MIBI ???????)? ??????RI???
???????? ???????????????????????? ?????????????
(99mTc-MIBI??????????(????????)????)
43
(No Transcript)
44
123I-IMP Brain SPECT FBP with Ramp
filter
45
123I-IMP Brain SPECT FBP with SheppLogan filter
46
?????? 18F-FDG ?PET ??????
?PET????????????????? ?????????
47
?PET???????? Ramp????? ????????? FBP??
48
??????? ???????? ?HP????