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Statistical Computing in Nuclear Imaging
book

Statistical Computing in Nuclear Imaging

by Arkadiusz Sitek
December 2014
Intermediate to advanced content levelIntermediate to advanced
275 pages
9h 12m
English
CRC Press
Content preview from Statistical Computing in Nuclear Imaging
Statistical computing 189
i i
i
i
State s State s + 1
y
ki
, c
i
y
ki
, c
i
y
ki
+ 1, c
i
+ 1
y
ki
1, c
i
1
y’s and c’s for other voxels are unchanged between s + 1 and s
FIGURE 6.4 Two subsequent states in the OE algorithm Markov chain if the “move”
is successful. Squares represent voxels.
List of Metropolis-Hastings acceptance ratios
F
lat prior:
x
F 1
=
(c
i
+ 1 )ǫ
i
c
i
ǫ
i
(6.32)
x
F 2
=
α
ki
(c
i
+ 1 )ǫ
i
α
ki
c
i
ǫ
i
(6.33)
Gamma prior:
x
G1
=
(c
i
+ ϑ
i
ω
i
)(ǫ
i
+ ω
i
)
(c
i
+ ϑ
i
ω
i
1 )(ǫ
i
+ ω
i
)
(6.34)
x
G2
=
α
ki
(c
i
+ ϑ
i
ω
i
)(ǫ
i
+ ω
i
)
α
ki
(c
i
+ ϑ
i
ω
i
1 )(ǫ
i
+ ω
i
)
(6.35)
Jeffreys prior:
x
J1
=
c
i
+
1
2
ǫ
i
c
i
1
2
ǫ
i
(6.36)
x
J2
=
α
ki
c
i
+
1
2
ǫ
i
α
ki
c
i
1
2
ǫ
i
(6.37)
Entropy pri or:
x
E1
=
ǫ
i
ǫ
i
c
i
+ 1
c
i
1β
(6.38)
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Publisher Resources

ISBN: 9781439849347