Genetical Algorithm(GA) for Sparse CT Image Reconstruction.

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Kazuma Nagafune

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Background of my study

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Before talk of GA

Computed Tomography(CT)

A technique of reconstructing section image.

1. Project to object ALL directions

2. Caluculate for respective throughed quantity

Problems

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IF num of projections are few(Sparse CT) →Can not reconstruct perfectly.

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Benefits

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IF we can solve Sparse CT →Get knowledges some structures of the object.

Arrange problems

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Projection needs ALL directions Obstacle might be there

=Sparse CT

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Arrange problems

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Projection needs ALL directions Obstacle might be there.

=Sparse CT We want to reconstruct even if our data is lacked.

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Projection needs ALL directions

Arrange problems

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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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fi :=Objective function(i=1,2,…n) := individuals

Genetical Algorithm(GA)

• Optimize Multi objective functions

• Exploitate using multi individuals

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Fllow chart f1

f２

Minimize (Maximum)

Objective functions

GS algorithm

Minimum problem

fi :=Objective function(i=1,2,…n) := individuals

Genetical Algorithm(GA)

• Optimize Multi objective functions

• Exploitate using multi individuals

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Fllow chart f1

f２

Minimize (Maximum)

Objective functions

GS algorithm

Minimum problem

fi :=Objective function(i=1,2,…n) := individuals

Genetical Algorithm(GA)

• Optimize Multi objective functions

• Exploitate using multi individuals

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Fllow chart f1

f２

Minimize (Maximum)

Objective functions

GS algorithm

Minimum problem

Explain the outline of GA

for Real number, NSGA-II[Deb, 2002]

GA is a one of the concenpt of

Evolutionary Multi-criterion Optimization(EMO).

Initialization

• Make individuals

– They are ramdomly.

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Fllow chart

GS algorithm

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f２

f1

Evaluation and Selection

• Individuals are evaluated and selected

– Related limited conditions

– f1, f2 have different limited conditions

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Fllow chart

GS algorithm

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f２

f1

GA operator

• Brush up them using GA-operator

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Fllow chart

GS algorithm

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Parent1 Parent2

Child1 Child2

ああああ Mutation

GA operator

• Genetical Algorithm(GA) operator

– Brush up them using GA-operator

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Fllow chart

GS algorithm

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Parent1 Parent2

Child1 Child2

ああああ Mutation

In my study, I had cogitated and equipped GA-operator in Japan. (But I’m not going to explain this in this presentation).

Crossover

• Crossover selected individuals(parents) – Set variety feautures to children

from parents’s.

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Fllow chart

GS algorithm

Parent1 Parent2

Child1 Child2

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Mutation

• Some time mutate a few individuals in the population

– Expect quiet new individual.

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Fllow chart

GS algorithm

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ああああ Mutation

Evaluation and one aalgorithm

• Evaluate Individuals

• Apply one algorithm

• Checek for terminate

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Talk about my case of study considering adobe explanation.

Fllow chart

GS algorithm

My case of study

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Fourier

Transform

Real space

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Frequency space

• 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.

Use all pixels of frequency space for individual’s genes.

Sparse CT is a inverse problem

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Lacked data will not know even if GOD.

Given data is very few.

Given data

Lacked data

To trace is quiet difficult.

Because given data is very few.

Sparse CT is a inverse problem

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Sparce CT (inverse problem) is inperfect problem,

so observer can not reconstruct original image perfectly.

Original image Reconstructed image

Numerical experience

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・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

Num of GS algorithm

10/20

10/20

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Original image

Projections

Table 1. each parameter

推定対象画像

Interior a watch

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Phantom

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Result

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Reconstructed result for 8 projections .

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Supposed Previous work Original

Result

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Reconstructed result for 20 projections .

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Supposed Previous work Original

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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