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MAPEM.ppsx
1.
2. Reconstruct an Image using Projection
Maximum A Posteriori Expectation
Maximization (MAPEM)
Optimizing the Iteration
Reducing the time
Performance Analysis –Amdahl’s Law.
3. Mathematical Process
Data obtained at various angles
Medical imaging modalities
◦ CT scan
◦ PET
◦ MRI scan
5. Analytical
◦ Filtered Back Projection (FBP)
Iterative
◦ Algebraic Reconstruction Technique (ART)
◦ Statistical Reconstruction Technique
Weighted Least Square
Likelihood based iterative Expectation Maximization
Maximum Likelihood Expectation Maximization
Maximum A Posteriori Expectation Maximization
6. Projection is a line integral along the path:
cos
sin
where
y)ds
f(x,
)
( y
x
s
t
p
AB
7. Projections with
different angles
are stored in
sinogram (raw
data)
Each horizontal
line in sinogram is
a projection
with different
angle
)
(t
p
projection )
(t
p
9. Multi-core platform
◦ Thread level parallelism
Simultaneous Multi-Threading (SMT)
Chip Multi-Processor (CMP)
Multi Core
Many Core
◦ Two conclusions for applications running on multi-
core platform
Conclusion 1. When multiple applications are executed,
the performance on multi-core platform is better than
single-core platform with the same clock frequency.
Conclusion 2. Applications without parallelization can’t
make full use of computing power on multi-core
platform.
OpenMP (OMP) directives is implemented
10. Amdahl’s Law
◦ statement of the maximum theoretical speed-up
you casn ever hope to achieve.
time
execution
Parallel
time
execution
Sequential
Speedup
f
n
f
f
p
S
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