- Email: [email protected]
Improved Interscale-Based SURE-LET Approach to Image Denoising
Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 107 (2017) 819 – 823
,QWHUQDWLRQDO &RQJUHVV RI ,QIRUPDWLRQ DQG &RPPXQLFDWLRQ 7HFKQRORJ\ ,&,&7
,PSURYHG ,QWHUVFDOH%DVHG 685(/(7 $SSURDFK WR ,PDJH 'HQRLVLQJ ;LDRER =KDQJD D
,QVWLWXWH RI *UDSKLFV DQG ,PDJH 3URFHVVLQJ ;LDQ\DQJ 1RUPDO 8QLYHUVLW\ ;LDQ\DQJ &KLQD
&RUUHVSRQGLQJ DXWKRU ]KDQJ[LDRER #FRP 7HO
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
,QWURGXFWLRQ 'HQRLVLQJ RI LPDJH LV RQH LPSRUWDQW SUREOHP LQ WKH UHVHDUFK DQG DSSOLFDWLRQ RI LPDJH SURFHVVLQJ $PRQJ WKHVH PHWKRGV WKH 685( VWHLQ¶V XQELDVHG ULVN HVWLPDWH ±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
1877-0509 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 7th International Congress of Information and Communication Technology doi:10.1016/j.procs.2017.03.183
820
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823
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Ö RI [ ^[Q `Q !1 7KH :LHQHU ILOWHU LQ ZDYHOHW GRPDLQ LV SURSRVHG LQ >@ ,W FDQ EH H[SUHVVHG DV [ÖL
ZL \L
ZL
PD[^TL V ` PD[^TL V ` V
,Q DQG [Ö UHSUHVHQWV FRHIILFLHQWV RI WKH µFOHDQ¶ LPDJH ZDYHOHW FRHIILFLHQW V GHQRWHV WKH YDULDQFH RI QRLVH DQG TL LV REWDLQHG E\ DYHUDJLQJ WKH VTXDUHG YDOXH RI WKH ZDYHOHW FRHIILFLHQWV LQ QHLJKERXU ZLQGRZ FHQWHUHG DW WKH SURFHVVHG FRHIILFLHQW 7KH ZL LV WHUPHG WKH :LHQHU HVWLPDWRU 7KH [ÖL LV WKH EHVW OLQHDU HVWLPDWH RI VLJQDO FRPSRQHQW [L ,Q >@ WKH GHQRLVLQJ SHUIRUPDQFH FDQ EH LPSURYHG E\ LQWURGXFLQJ WKH UHPHG\ IDFWRU RI YDULDQFH ZKLFK EDODQFHV GHQRLVLQJ DPRXQW DQG GHWDLO SUHVHUYLQJ 6R WKH PRGLILHG :LHQHU ILOWHU WKH :LHQHUOLNH HVWLPDWRU LV H[SUHVVHG DV ZL
PD[^TL OV ` PD[^TL OV ` V
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³685( /(7´ VWUDWHJ\ LV FRQVLGHUHG DQG WKHQ WKLV PRGLILHG :LHQHU HVWLPDWRU LV LQWURGXFHG LQWR LPDJH GRPDLQ 685(/(7 SRLQWZLVH WKUHVKROGLQJ IXQFWLRQ EHORZ ,Q WKH IROORZLQJ WKH RUJLQDO LQWHUVFDOHEDVHG 685(/(7 DSSURDFK LV LPSURYHG 7KH SURSRVHG PHWKRG ,Q WKH RUWKRQRUPDO ZDYHOHW WUDQVIRUP WKH 06( PHDQ VTXDUH HUURU LQ WKH GRPDLQ RI LPDJH LV WKH ZHLJKWHG VXP RI 06( RI DOO GLIIHUHQW VXEEDQGV 6R WKH HVVHQWLDOLW\ RI WKH 685(/(7 DSSURDFK LQ PLQLPL]LQJ
H
1
1
¦ T Q
\Q \QT \Q V T c \Q
1
1
¦[
Q
Q
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
821
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823
QRUPDOL]DWLRQ * [ S H LV XVHG WR ILOWHU WKH DEVROXWH YDOXH RI WKH JURXS GHOD\ FRPSHQVDWLRQ RXWSXW $V ZLWK >@ WKH VREXLOW LQWHUVFDOH SUHGLFWRU E\ \S LV XVHG LQ WKH UHVW RI WKH SDSHU ,Q >@ 7KLHUU\ %OX DQG )ORULDQ /XLVLHU SURSRVHG WR XVH WKH \S WR GLVFULPLQDWH ZDYHOHW FRHIILFLHQWV ZLWK KLJK 6LJQDO1RLVH5DWLR DQG WKRVH ZLWK ORZ 6LJQDO 1RLVH5DWLR 7KHUHIRUH WKH JHQHUDO SRLQWZLVH GHQRLVLQJ IXQFWLRQ LV IRUPHG DV IROORZV [
.
.
N
N
I \ S ¦ DNM N \ I \ S ¦ ENM N \
T \
7KH VROXWLRQV RI WKH SDUDPHWHUV DN DQG EN DUH REWDLQHG E\ PLQLPL]LQJ WKH H )RU WKH SURSRVHG QHZ PHWKRG DV ZLWK >@ WKH JRRG UHVXOWV DUH DFKLHYHG ZLWK . %\ WDNLQJ WKH IXQFWLRQ
\ S 7
I \S
H
MN \
\H
DQG
N \ 7
V WKH SRLQWZLVH GHQRVLQJ IXQFWLRQ LV IRUPHG DV
ZLWK 7
T \ H
\ S 7
D D H
\ 7
DH
\ 7
\ H
%\ VXEVWLWXWLQJ \ LQ WKH H[SRQHQWLDO IXQFWLRQ LQ IRU LQWHUVFDOH DQG LQWUDVFDOH LQIRUPDWLRQ LV H[SUHVVHG DV
T \ H 7KH SDUDPHWHU
¦I
P
\ S 7
X
D D H
Z \ 7
X X X X X X
X
D H
Z \ 7
D X
E EH
\ 7
EH
\ 7
\
Z\ WKH SURSRVHG WKUHVKROGLQJ IXQFWLRQ LQWUHJUDWLQJ WKH
E X
E X
\ H
D X
\ IO \ XO \IP \ V IPc \
\ S 7
D X
\ S 7
E EH E
Z \ 7
EH
Z \ 7
\
FDQ EH VROYHG E\
O
ZKHUH P
I \
H
Z \ 7
XH
\ S 7
\
I \
\
XH
\ S 7
\ S 7
DQG I \ X H LW LV EHOLHYHG WKDW Z LV LQGHSHQGHQW RI \ I \ X H
\ S 7
H
Z \ H
Z \ 7
H \ I \ X H \ I \ XH $V ZLWK >@ LQ WKH FRPSXWDWLRQ RI GHULYDWLRQ RI IO
7
\
\ S 7
\
Z \ 7
\ S 7
7KH H[SHULPHQWDO UHVXOWV ,Q WKH H[SHULPHQW WKH HLJKW WHVW LPDJHV DUH WKH VL]H î RI $O %DUEDUD %RDW &URZG *ROGKLOO DQG WKH VL]H î RI 3HSSHUV +RXVH %ULGJH VL]H î LQ WXUQ 7KH H[SHULPHQW LV FDUULHG RXW DW HLJKW GLIIHUHQW DGGLWLYH *DXVVLDQ ZKLWH QRLVH OHYHOV >@ 6LQFH WKH FRUUHVSRQGLQJ 0DWODE FRGHV IRU WKH GLIIHUHQW PHWKRGV KDYH EHHQ JLYHQ LQ WKHLU UHVSHFWLYH DXWKRU¶V ZHEVLWHV WKH FRPSDULVRQ KHUH LV YHU\ VWDEOH DQG UHOLDEOH 7DEOH &RPSDULVRQ RI GHQRLVLQJ UHVXOWV E\ RULJLQDO 685(/(7 DSSURDFK >@ DQG SURSRVHG PHWKRG LQ 3615 V 0HWKRG 685(/(7 3URSRVHG
3HSSHUV
+RXVH
822
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823 0HWKRG 685(/(7 3URSRVHG 0HWKRG 685(/(7 3URSRVHG 0HWKRG 685(/(7 3URSRVHG
$O %DUEDUD &RZG
D
E
F
G
%ULGJH %RDW *ROGKLOO
)LJ &RPSDULVRQ RI GHQRLVLQJ UHVXOWV D 1RLVHIUHH %DUEDUD E 1RLV\ %DUEDUD V F 'HQRLVLQJ UHVXOW XVLQJ RULJLQDO 685(/(7 DSSURDFK >@ G 'HQRLVLQJ UHVXOW XVLQJ WKH SURSRVHG DSSURDFK
,Q WKH WHVW DV ZLWK >@ WKH ³V\P´ ZLWK WKH VDPH GHFRPSRVLWLRQ OHYHOV LV XVHG 6TXDUHVKDSH ZLQGRZ VL]H IRU WKH ILUVW GHFRPSRVLWLRQ OHYHO DQG WKH VHFRQG GHFRPSRVLWLRQ OHYHO DQG WKH WKLUG GHFRPSRVLWLRQ OHYHO LV î DQG î DQG î UHVSHFWLYHO\ 6TXDUHVKDSH ZLQGRZ VL]H IRU WKH UHVW RI GHFRPSRVLWLRQ OHYHOV LV î )URP 7DEOH LW FDQ EH VHHQ WKDW WKH QHZ PHWKRG REWDLQV WKH KLJKHU YDOXHV LQ 3615 LQ RI FDVHV FRPSDUHG WR WKH RULJLQDO LQWHUVFDOH
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823
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
823
ScienceDirect Procedia Computer Science 107 (2017) 819 – 823
,QWHUQDWLRQDO &RQJUHVV RI ,QIRUPDWLRQ DQG &RPPXQLFDWLRQ 7HFKQRORJ\ ,&,&7
,PSURYHG ,QWHUVFDOH%DVHG 685(/(7 $SSURDFK WR ,PDJH 'HQRLVLQJ ;LDRER =KDQJD D
,QVWLWXWH RI *UDSKLFV DQG ,PDJH 3URFHVVLQJ ;LDQ\DQJ 1RUPDO 8QLYHUVLW\ ;LDQ\DQJ &KLQD
&RUUHVSRQGLQJ DXWKRU ]KDQJ[LDRER #FRP 7HO
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
,QWURGXFWLRQ 'HQRLVLQJ RI LPDJH LV RQH LPSRUWDQW SUREOHP LQ WKH UHVHDUFK DQG DSSOLFDWLRQ RI LPDJH SURFHVVLQJ $PRQJ WKHVH PHWKRGV WKH 685( VWHLQ¶V XQELDVHG ULVN HVWLPDWH ±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
1877-0509 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 7th International Congress of Information and Communication Technology doi:10.1016/j.procs.2017.03.183
820
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823
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Ö RI [ ^[Q `Q !1 7KH :LHQHU ILOWHU LQ ZDYHOHW GRPDLQ LV SURSRVHG LQ >@ ,W FDQ EH H[SUHVVHG DV [ÖL
ZL \L
ZL
PD[^TL V ` PD[^TL V ` V
,Q DQG [Ö UHSUHVHQWV FRHIILFLHQWV RI WKH µFOHDQ¶ LPDJH ZDYHOHW FRHIILFLHQW V GHQRWHV WKH YDULDQFH RI QRLVH DQG TL LV REWDLQHG E\ DYHUDJLQJ WKH VTXDUHG YDOXH RI WKH ZDYHOHW FRHIILFLHQWV LQ QHLJKERXU ZLQGRZ FHQWHUHG DW WKH SURFHVVHG FRHIILFLHQW 7KH ZL LV WHUPHG WKH :LHQHU HVWLPDWRU 7KH [ÖL LV WKH EHVW OLQHDU HVWLPDWH RI VLJQDO FRPSRQHQW [L ,Q >@ WKH GHQRLVLQJ SHUIRUPDQFH FDQ EH LPSURYHG E\ LQWURGXFLQJ WKH UHPHG\ IDFWRU RI YDULDQFH ZKLFK EDODQFHV GHQRLVLQJ DPRXQW DQG GHWDLO SUHVHUYLQJ 6R WKH PRGLILHG :LHQHU ILOWHU WKH :LHQHUOLNH HVWLPDWRU LV H[SUHVVHG DV ZL
PD[^TL OV ` PD[^TL OV ` V
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³685( /(7´ VWUDWHJ\ LV FRQVLGHUHG DQG WKHQ WKLV PRGLILHG :LHQHU HVWLPDWRU LV LQWURGXFHG LQWR LPDJH GRPDLQ 685(/(7 SRLQWZLVH WKUHVKROGLQJ IXQFWLRQ EHORZ ,Q WKH IROORZLQJ WKH RUJLQDO LQWHUVFDOHEDVHG 685(/(7 DSSURDFK LV LPSURYHG 7KH SURSRVHG PHWKRG ,Q WKH RUWKRQRUPDO ZDYHOHW WUDQVIRUP WKH 06( PHDQ VTXDUH HUURU LQ WKH GRPDLQ RI LPDJH LV WKH ZHLJKWHG VXP RI 06( RI DOO GLIIHUHQW VXEEDQGV 6R WKH HVVHQWLDOLW\ RI WKH 685(/(7 DSSURDFK LQ PLQLPL]LQJ
H
1
1
¦ T Q
\Q \QT \Q V T c \Q
1
1
¦[
Q
Q
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
821
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823
QRUPDOL]DWLRQ * [ S H LV XVHG WR ILOWHU WKH DEVROXWH YDOXH RI WKH JURXS GHOD\ FRPSHQVDWLRQ RXWSXW $V ZLWK >@ WKH VREXLOW LQWHUVFDOH SUHGLFWRU E\ \S LV XVHG LQ WKH UHVW RI WKH SDSHU ,Q >@ 7KLHUU\ %OX DQG )ORULDQ /XLVLHU SURSRVHG WR XVH WKH \S WR GLVFULPLQDWH ZDYHOHW FRHIILFLHQWV ZLWK KLJK 6LJQDO1RLVH5DWLR DQG WKRVH ZLWK ORZ 6LJQDO 1RLVH5DWLR 7KHUHIRUH WKH JHQHUDO SRLQWZLVH GHQRLVLQJ IXQFWLRQ LV IRUPHG DV IROORZV [
.
.
N
N
I \ S ¦ DNM N \ I \ S ¦ ENM N \
T \
7KH VROXWLRQV RI WKH SDUDPHWHUV DN DQG EN DUH REWDLQHG E\ PLQLPL]LQJ WKH H )RU WKH SURSRVHG QHZ PHWKRG DV ZLWK >@ WKH JRRG UHVXOWV DUH DFKLHYHG ZLWK . %\ WDNLQJ WKH IXQFWLRQ
\ S 7
I \S
H
MN \
\H
DQG
N \ 7
V WKH SRLQWZLVH GHQRVLQJ IXQFWLRQ LV IRUPHG DV
ZLWK 7
T \ H
\ S 7
D D H
\ 7
DH
\ 7
\ H
%\ VXEVWLWXWLQJ \ LQ WKH H[SRQHQWLDO IXQFWLRQ LQ IRU LQWHUVFDOH DQG LQWUDVFDOH LQIRUPDWLRQ LV H[SUHVVHG DV
T \ H 7KH SDUDPHWHU
¦I
P
\ S 7
X
D D H
Z \ 7
X X X X X X
X
D H
Z \ 7
D X
E EH
\ 7
EH
\ 7
\
Z\ WKH SURSRVHG WKUHVKROGLQJ IXQFWLRQ LQWUHJUDWLQJ WKH
E X
E X
\ H
D X
\ IO \ XO \IP \ V IPc \
\ S 7
D X
\ S 7
E EH E
Z \ 7
EH
Z \ 7
\
FDQ EH VROYHG E\
O
ZKHUH P
I \
H
Z \ 7
XH
\ S 7
\
I \
\
XH
\ S 7
\ S 7
DQG I \ X H LW LV EHOLHYHG WKDW Z LV LQGHSHQGHQW RI \ I \ X H
\ S 7
H
Z \ H
Z \ 7
H \ I \ X H \ I \ XH $V ZLWK >@ LQ WKH FRPSXWDWLRQ RI GHULYDWLRQ RI IO
7
\
\ S 7
\
Z \ 7
\ S 7
7KH H[SHULPHQWDO UHVXOWV ,Q WKH H[SHULPHQW WKH HLJKW WHVW LPDJHV DUH WKH VL]H î RI $O %DUEDUD %RDW &URZG *ROGKLOO DQG WKH VL]H î RI 3HSSHUV +RXVH %ULGJH VL]H î LQ WXUQ 7KH H[SHULPHQW LV FDUULHG RXW DW HLJKW GLIIHUHQW DGGLWLYH *DXVVLDQ ZKLWH QRLVH OHYHOV >@ 6LQFH WKH FRUUHVSRQGLQJ 0DWODE FRGHV IRU WKH GLIIHUHQW PHWKRGV KDYH EHHQ JLYHQ LQ WKHLU UHVSHFWLYH DXWKRU¶V ZHEVLWHV WKH FRPSDULVRQ KHUH LV YHU\ VWDEOH DQG UHOLDEOH 7DEOH &RPSDULVRQ RI GHQRLVLQJ UHVXOWV E\ RULJLQDO 685(/(7 DSSURDFK >@ DQG SURSRVHG PHWKRG LQ 3615 V 0HWKRG 685(/(7 3URSRVHG
3HSSHUV
+RXVH
822
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823 0HWKRG 685(/(7 3URSRVHG 0HWKRG 685(/(7 3URSRVHG 0HWKRG 685(/(7 3URSRVHG
$O %DUEDUD &RZG
D
E
F
G
%ULGJH %RDW *ROGKLOO
)LJ &RPSDULVRQ RI GHQRLVLQJ UHVXOWV D 1RLVHIUHH %DUEDUD E 1RLV\ %DUEDUD V F 'HQRLVLQJ UHVXOW XVLQJ RULJLQDO 685(/(7 DSSURDFK >@ G 'HQRLVLQJ UHVXOW XVLQJ WKH SURSRVHG DSSURDFK
,Q WKH WHVW DV ZLWK >@ WKH ³V\P´ ZLWK WKH VDPH GHFRPSRVLWLRQ OHYHOV LV XVHG 6TXDUHVKDSH ZLQGRZ VL]H IRU WKH ILUVW GHFRPSRVLWLRQ OHYHO DQG WKH VHFRQG GHFRPSRVLWLRQ OHYHO DQG WKH WKLUG GHFRPSRVLWLRQ OHYHO LV î DQG î DQG î UHVSHFWLYHO\ 6TXDUHVKDSH ZLQGRZ VL]H IRU WKH UHVW RI GHFRPSRVLWLRQ OHYHOV LV î )URP 7DEOH LW FDQ EH VHHQ WKDW WKH QHZ PHWKRG REWDLQV WKH KLJKHU YDOXHV LQ 3615 LQ RI FDVHV FRPSDUHG WR WKH RULJLQDO LQWHUVFDOH
Xiaobo Zhang / Procedia Computer Science 107 (2017) 819 – 823
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
823