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Human Systems Lab., Dept. of Systems Science Graduate School of Informatics, Kyoto University

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l l l l l l Computed Tomography l

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Fourier 3

Jean Baptiste Joseph Fourier (17681830)

, 1822

1768 1795 1798 1802 1822 1827 1830 63

4

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sin(1) 5

-2

-1

0

1

2 N=2

-2

-1

0

1

2

N=5

-2

-1

0

1

2

N=10

-2

-1

0

1

2

M=2

sin(2) 6

-2

-1

0

1

2

M=5

-2

-1

0

1

2

M=10

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7

2 f(x)

(1) 8

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(2) 9

(3) 10

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-2

-1

0

1

2 M=10

(4) 11

12

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Outline 13

l l l l l l Computed Tomography l

(1) 14

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(2) 15

(3) 16

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(4) 17

18

2 f (x) g(x)

f (x) g(x)

a b aTb = 0

ab

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1. 0 2. 0

19

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l l l l l l Computed Tomography l

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(1) 21

f (x) cos mx

(2) 22

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Outline 23

l l l l l l Computed Tomography l

24

2L f(x)

an =1

L

Z 2L

0f(x) cos

nx

L

dx

bn =1

L

Z 2L

0f(x) sin

nx

L

dx

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25

f (x)

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l l l l l l Computed Tomography l

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Computed Tomography CT 27

CT

CTXX

http://www.toshiba-medical.co.jp/tmd/products/ct/index.html

CT 28

X),( yxf

),( XR

f (x,y)

R(X,)

),( wvG

X y

x

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Outline 29

l l l l l l Computed Tomography l

30

1. M = 2, 5, 10 f (x)

2.