2. Before talk of GA
Background of my study
Computed Tomography(CT)
A technique of reconstructing section image.
1. Project to object ALL directions
2. Caluculate for respective throughed quantity
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3. Problems
IF num of projections are few(Sparse CT)
→Can not reconstruct perfectly.
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4. Benefits
IF we can solve Sparse CT
→Get knowledges some structures of the object.
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6. Arrange problems
Projection needs ALL directions
Obstacle might be there.
=Sparse CT
We want to reconstruct
even if our data is lacked.
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7. Arrange problems
Projection needs ALL directions
Projection needs ALL directions
Obstacle might be there.
=Sparse CT
We want to reconstruct
even if our data is lacked.
Approach applying
Genetical Algorithm(GA)
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8. Genetical Algorithm(GA)
• Optimize Multi objective functions
• Exploitate using multi individuals
:= individuals
fi :=Objective function(i=1,2,…n)
f２
GS algorithm
f1
Minimize (Maximum)
Objective functions
Fllow chart
Minimum problem
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9. Genetical Algorithm(GA)
• Optimize Multi objective functions
• Exploitate using multi individuals
:= individuals
fi :=Objective function(i=1,2,…n)
f２
GS algorithm
f1
Minimize (Maximum)
Objective functions
Fllow chart
Minimum problem
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10. Genetical Algorithm(GA)
• Optimize Multi objective functions
• Exploitate using multi individuals
Explainf :=Objective function(i=1,2,…n)
the outline of GA
:= individuals
f
for Real number,
NSGA-II[Deb, 2002]
i
２
GS algorithm
GA is a one of the concenpt of
Evolutionary Multi-criterion Optimization(EMO).
f1
Minimize (Maximum)
Objective functions
Fllow chart
Minimum problem
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12. Evaluation and Selection
• Individuals are
evaluated and selected
– Related limited conditions
– f1, f2 have different limited
conditions
GS algorithm
f２
Fllow chart
f1
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13. GA operator
• Brush up them using GAoperator
あ
あ
あ
あ
Mutation
GS algorithm
Parent1
Parent2
Child1
Child2
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Fllow chart
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14. GA operator
• Genetical Algorithm(GA) operator
– Brush up them using GAoperator
あ
あ
あ
あ
In my study, I had cogitated and
Mutation
equipped GA-operator in Japan.
Parent1
Parent2
(But I’m not going to explain this in
this presentation).
Child1
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Child2
GS algorithm
Fllow chart
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16. Mutation
• Some time mutate a few
individuals in the population
– Expect quiet new individual.
あ
あ
あ
あ
Mutation
GS algorithm
Fllow chart
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17. Evaluation and one aalgorithm
• Evaluate Individuals
• Apply one algorithm
• Checek for terminate
GS algorithm
Talk about my case of study
considering adobe explanation.
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Fllow chart
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18. My case of study
Fourier
Transform
Real space
Frequency space
Use all pixels of frequency space for individual’s genes.
• One image has two individuals
– Real part and Imaginary part of frequency space)
• If 256 x 256pixels image, one individul has
65536 x 2 genes.
– Too much genes will have to be brushed up.
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19. Sparse CT is a inverse problem
To trace is
quiet difficult.
Because
given data is
very few.
Given data
Given data is very few.
Lacked data
Lacked data will not know even if GOD.
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20. Sparse CT is a inverse problem
Sparce CT (inverse problem) is inperfect problem,
so observer can not reconstruct original image perfectly.
Original image
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Reconstructed image
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21. Numerical experience
・EMO algorithm：for realnumber,NSGA-II
・generation：30
・Original image：Phantom,Interior of watch
・Projections：8(phantom),20(watch)
・Each parameter (Phantom/LENA) ：Table 1
Table 1. each parameter
Original image
10/20
Num of GS algorithm
Projections
10/20
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25. Summarize
The outcomes
• I have conducted on toys I have achieved
favorable results.
• I could show the efficacy utilizing GA-operator
Another cahllanges
• Include some noises from given data
• Utilize results another previous work
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