Restoration

3102/3/21

1 azerruoP .R.H

:

AZERRUOP .R.H

2222

3102/3/21

2 azerruoP .R.H

::::

evitcejbus )

(

: evitcejbo

AZERRUOP .R.H

3333

% #"

(gnision-ed) : :

)y,x( )y,x(h )y,x( +)y,x(f*)y,x(h=)y,x(g

)y,x(f )y,x(g * h )y,x(f

)v,u(N+)v,u(F)v,u(H=)v,u(G:

)y,x( +)y,x(f=)y,x(g)y,x(f*)y,x(h=)y,x(g

)y,x(+)y,x(f*)y,x(h=)y,x(g

AZERRUOP .R.H

4444

3102/3/21

3 azerruoP .R.H

% #"

AZERRUOP .R.H

5555

*)( '&:

( H) eslupmi h

.

.

( ) ( ). ( )

AZERRUOP .R.H

6666

0 (,)(,)(,)(,)1

0

1

0axystsxtyNxy

N

t

M

s

==

=

=

3102/3/21

4 azerruoP .R.H

'& ,+*)( '& 2

. ])+(,)-([ z % 07. ])2+(,)2-([ z % 59

AZERRUOP .R.H

7777

()/2 22

2 ()1

pi

=pzez

'& ,+*)( '&

AZERRUOP .R.H

8888

3102/3/21

5 azerruoP .R.H

)hgielyaR('& - *)( '&

:

b a

AZERRUOP .R.H

9999

2

. 2L < 2

2L > 2

AZERRUOP .R.H

23232323

2 (,)(,)[(,)]2

LL

= fxygxygxym

2si ot tes eb 12

L

3102/3/21

71 azerruoP .R.H

`^_O=N Yg \ [Z YXW '&

AZERRUOP .R.H

33333333

`^_O=N Yg \ [Z YXW '&

yxS : nimZyxS : xamZyxS : demZ)y,x( : yxZ

yxS : xamS

AZERRUOP .R.H

43434343

3102/3/21

81 azerruoP .R.H

`^_O=N Yg \ [Z YXW '&

: nimZ demZ =1A xamZ demZ =2A () ,0 < 2A 0 > 1A

xamS = 1B

demZ=

AZERRUOP .R.H

53535353

demZ .

demZ .

`^_O=N Yg \ [Z YXW '&

AZERRUOP .R.H

63636363

3102/3/21

91 azerruoP .R.H

*)( '& KJC \ [Z YXW '& hcton) ( ssapdnab) (tcejerdnab)

( retlif

.

.

AZERRUOP .R.H

73737373

*)( '& KJC \ [Z YXW '&

AZERRUOP .R.H

83838383

+=

esiwrehto

fiDWDuvDWHuv

12

(,)2

00 (,)0

12/3/2013

H.R. Pourreza 20

&' WXY Z[ \ CJK &' ()*

H.R. POURREZA

39393939

n

DvuDWvuD

vuH 2

20

2 ),(),(1

1),(

+

=

n =1

&' WXY Z[ \ CJK &' ()*

H.R. POURREZA

40404040

=WvuDDvuD

evuH ),(),( 202

1),(

12/3/2013

H.R. Pourreza 21

&' WXY Z[ \ CJK &' ()*

H.R. POURREZA

41414141

&' WXY Z[ \ CJK &' ()* :

H.R. POURREZA

42424242

),(1),( vuHvuH brbp =

3102/3/21

22 azerruoP .R.H

*)( '& KJC \ [Z YXW '& : hctoN

. .

AZERRUOP .R.H

34343434

*)( '& KJC \ [Z YXW '& hctoN

AZERRUOP .R.H

44444444

12/3/2013

H.R. Pourreza 23

&' WXY Z[ \ CJK &' ()* Notch

H.R. POURREZA

45454545

n=2

&' WXY Z[ \ CJK &' ()* Notch

H.R. POURREZA

46464646

3102/3/21

42 azerruoP .R.H

*)( '& KJC \ [Z YXW '& PN RN : hctoN

AZERRUOP .R.H

74747474

= pnrn HuvHuv (,)1(,)


AZERRUOP .R.H

84848484

PN

PN

RN

3102/3/21

52 azerruoP .R.H

*)( '& KJC \ [Z YXW '& hctoN

AZERRUOP .R.H

94949494


.

AZERRUOP .R.H

05050505

= fxygxyxy (,)(,)(,)

= fxygxyxy (,)(,)(,)= xyTFIHuvGuv (,)(,)(,)} {

3102/3/21

62 azerruoP .R.H


:

)y,x( )1+b2( )1+a2(

. )y,x(

AZERRUOP .R.H

15151515

= fxygxywxyxy (,)(,)(,)(,)

= =

++++

=

a

sa

b

tbfxsytfxy

abxy

2(21()21)(,)(,) 2

(,)1

= =

++++

=

a

sa

b

tbfxsyt

ab(21()21)(,) fxy

(,)1


:

AZERRUOP .R.H

25252525

(,)(,) ++= wxsytwxyrofasadnabtb

2

2

[(,)(,)(,}](,)(,])

(21()21)[{(,)(,)1

gxywxyxy

wxsytxsyt

gxsytab

xya

sa

b

tb

++++

++++

== =

= wxyxywxyxy (,)(,)(,)(,)

12/3/2013

H.R. Pourreza 27

&' WXY Z[ \ CJK &' ()* Notch ...

2(x,y)

H.R. POURREZA

53535353

2

2

)},(),(),([)],(),(

),({[)12)(12(1),(

yxyxwyxg

tysxtysxw

tysxgba

yx aas

b

bt

++++

++++

= =

=

0),(),(2

=

yxwyx

),(),(),(),(),(),(),(

22 yxyxyxyxgyxyxgyxw

=

&' WXY Z[ \ CJK &' ()* Notch ...

H.R. POURREZA

54545454

),(),(),(),( yxyxwyxgyxf =),( yxw),( yx),( yxg

12/3/2013

H.R. Pourreza 28

&' WXY Z[ \ CJK &' ()* Notch ...

H.R. POURREZA

55555555

&' WXY Z[ \ CJK &' ()* Notch ...

H.R. POURREZA

56565656

3102/3/21

92 azerruoP .R.H

*)( '& KJC \ [Z YXW '& ... hctoN

AZERRUOP .R.H

75757575

fxy (,) gxy (,)215x215:

51=b=a

\ i [Z '&

: : Hb a

: H

AZERRUOP .R.H

85858585

=+ gxyHfxyxy (,)[(,])(,)

+=+ HafxybfxyaHfxybHfxy 1212 [(,)(,])[(,])[(,])

gxyHfxyHfxygxy == (,)[(,])[(,])(,)

3102/3/21

03 azerruoP .R.H

\ i [Z '& ...

. noitulovnoced

AZERRUOP .R.H

95959595

+

+

gxyfhxyddxy (,)(,)(,)(,) =+

(,)(,)(,)(,)(,)(,)*(,)(,)

GuvHuvFuvNuvgxyhxyfxyxy

=+

=+

VUTSR % #" - \ i [Z '&

AZERRUOP .R.H

06060606

3102/3/21

13 azerruoP .R.H

VUTSR % #" - \ i [Z '&

( )

.

AZERRUOP .R.H

16161616

AGuv

= (,)(,) Huv

VUTSR % #" - \ i [Z '&

. )y,x(sg

. )v,u(H

AZERRUOP .R.H

26262626

sfxy (,)

(,)(,)(,)

FuvGuv

Huvs

s= s

3102/3/21

23 azerruoP .R.H

VUTSR % #" - \ i [Z '&

AZERRUOP .R.H

36363636

=+ Huvekuv (,)() 225/6

: 100.0=k

: 5200.0=k

: 52000.0=k

VUTSR % #" - \ i [Z '&

)sneL nihT( P P

AZERRUOP .R.H

46464646

snel nihT

sucof thgiR sucof tfeL

d retemaid sneLf htgnel lacoF

3102/3/21

33 azerruoP .R.H

VUTSR % #" - \ i [Z '&

)sneL nihT( :

AZERRUOP .R.H

56565656

fuv111

=+

v u

VUTSR % #" - \ i [Z '&

)y,x(h . )y,x(h . )v,u(H

AZERRUOP .R.H

66666666

12/3/2013

H.R. Pourreza 34

&' Z[ i \ - "# % RSTUV

H.R. POURREZA

67676767

=T

dttyytxxfyxg0

00 )](),([),(

uaj

TTuat

euaua

T

dtevuH

pi

pi

pipi

=

=

)sin(

),(0

/2== 0)(/)( 00 tyandTattxif

dtevuFvuGT

tvytuxj

+=

0

)]()([2 00),(),( pi

dtevuHT

tvytuxj

+=

0

)]()([2 00),( pi

&' Z[ i \ - "# % RSTUV

H.R. POURREZA

68686868

)()](sin[)(),(vbuajevbua

vbuaT

vuH +++

=pipi

pi

== TbttyandTattxif /)(/)( 00

3102/3/21

53 azerruoP .R.H

`^_O= lk - \ i [Z '&

AZERRUOP .R.H

96969696

(,)(,)(,)

HuvGuv

= Fuv

(,)(,)(,)(,)

HuvNuv

=+ FuvFuv

F H/N .

.

`^_O= lk - \ i [Z '&

AZERRUOP .R.H

07070707

04

07

58

3102/3/21

63 azerruoP .R.H

(`^_O= sr=)`^_O= qp feol nm - \ i [Z '& .

AZERRUOP .R.H

17171717

= eEff 22 ([)]

esion dna egamI modnar erassecorp

. 2e f

(`^_O= sr=)`^_O= qp feol nm - \ i [Z '&

AZERRUOP .R.H

27272727

(,)(,)(,)/(,)

(,)(,)

1

(,)(,)(,)/(,)

(,)

(,)(,)(,)(,)

(,)(,)(,)

2

2

2

*

2

*

GuvHuvSuvSuv

HuvHuv

GuvHuvSuvSuv

Huv

GuvSuvHuvSuv

HuvSuvFuv

f

f

f

f

+=

+=

+=

= SuvNuv (,)(,)2= f SuvFuv (,)(,)2

.

12/3/2013

H.R. Pourreza 37

&' Z[ i \ - mn loef pq =O_^`)=rs =O_^`(

H.R. POURREZA

73737373

),(),(/),(),(

),(),(

1),( 22

vuGvuSvuSvuH

vuHvuH

vuFf

+=

),(),(

),(),(

1),( 22

vuGKvuH

vuHvuH

vuF

+=

&' Z[ i \ - mn loef pq =O_^`)=rs =O_^`(

H.R. POURREZA

74747474

k

12/3/2013

H.R. Pourreza 38

&' Z[ i \ - mn loef pq =O_^`)=rs =O_^`(

H.R. POURREZA

75757575

&' Z[ i \ - 8tuvw :

H.R. POURREZA

76767676

=

=

=

=

= 1

0

1

0

2

1

0

1

0

2

),(

),(M

u

N

v

M

u

N

v

vuN

vuFSNR

[ ]=

=

=

1

0

1

0

2),(),(1M

u

N

v

yxfyxfMN

MSE

[ ]

=

=

=

=

= 1

0

1

0

2

1

0

1

0

2

),(),(

),(M

u

N

v

M

u

N

v

yxfyxf

yxfSNR

3102/3/21

93 azerruoP .R.H

AZERRUOP .R.H

77777777

noitcejorp-kcaB

AZERRUOP .R.H

87878787

2 1

23 4 3

3102/3/21

04 azerruoP .R.H

AZERRUOP .R.H

97979797

2 1

46 23 4

)TC(

AZERRUOP .R.H

08080808

3102/3/21

14 azerruoP .R.H

dyx - ),(

AZERRUOP .R.H

18181818

xy socnis +=

dyx -

.

AZERRUOP .R.H

28282828

(,)(,)(socnis) jkkkj gfxyxyydxd =+socnis += xy kkj

(,)(,)(socnis) gfxyxyydxd =+

fxy (,)} {

12/3/2013

H.R. Pourreza 42

- xyd

H.R. POURREZA

83838383

=

=

+=1

0

1

0)sincos(),(),(

M

x

N

y

yxyxfg

- xyd :

H.R. POURREZA

84848484

+

=

OtherwiseryxA

yxf0

),(222

=

=

dyyf

dxdyxyxfg

),(

)(),()0,(

o

3102/3/21

34 azerruoP .R.H

dyx - ... :

),(g r>|| r

12/3/2013

H.R. Pourreza 44

- xyd (Back-projection)

H.R. POURREZA

87878787

- xyd Fourier-slice

H.R. POURREZA

88888888

= pi degG j2),(),(

dydxeyxf

dydxdeyxyxf

ddydxeyxyxfG

yxj

j

j

+

=

+=

+=

)sincos(2

2

2

),(

)sincos(),(

)sincos(),(),(

pi

pi

pi

3102/3/21

54 azerruoP .R.H

dyx - ecils-reiruoF

nis =v soc =u

:

)ecilS( :

AZERRUOP .R.H

98989898

pisoc,nis

(,)(,)2()==

+

=

uv

Gfxyexdyd jxuyv

] [(soc,nis)

soc,nis (,)(,)

F

GFuvuv

=

===

dyx - ecils-reiruoF

)ecilS( :

)v,u(F

AZERRUOP .R.H

09090909

3102/3/21

64 azerruoP .R.H

dyx - (: )

( ) ( ) ||

AZERRUOP .R.H

19191919

pifxyGedd pi

xy

j

0socnis

(,)(,)2=+

=

dyx - ...(: )

AZERRUOP .R.H

29292929

3102/3/21

74 azerruoP .R.H

dyx - : ...

AZERRUOP .R.H

39393939

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