This document discusses using a genetic algorithm (GA) to solve the problem of sparse computed tomography (CT) image reconstruction. Sparse CT occurs when there are few projection data points, making it difficult to perfectly reconstruct an image. The author proposes applying GA techniques like optimization of multiple objective functions, exploitation of multiple individuals, and genetic operators like crossover and mutation. As a test case, the author reconstructs phantom and interior watch images from limited projection data using their GA method, achieving favorable results compared to previous work. Further challenges are noted around adding noise to data and comparing to other reconstruction techniques.

1. Genetical Algorithm(GA)
for Sparse CT Image Reconstruction.
Kazuma Nagafune
3.10.2013
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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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5. Arrange problems
Projection needs ALL directions
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Obstacle might be there
=Sparse CT
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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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11. Initialization
• Make individuals
– They are ramdomly.
GS algorithm
f２
Fllow chart
f1
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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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15. Crossover
• Crossover
selected individuals(parents)
– Set variety feautures to children
from parents’s.
GS algorithm
Parent1
Parent2
Fllow chart
Child1
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Child2
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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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22. 推定対象画像
Interior a watch
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Phantom
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23. Result
Reconstructed result for 8 projections .
Previous work
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Supposed
Original
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24. Result
Reconstructed result for 20 projections .
Previous work
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Supposed
Original
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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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