图像的频域倒数_高斯级联低通滤波去噪方法

图像的频域倒数_高斯级联低通滤波去噪方法 Vol. 29 No. 1229 12 ?? ???? ???? ?? ?? ?? ?? ?? ??Dec. 20122012 cato Research of Comters12 Appliinpu?? ?? *-??????????????????????????????????E?E? ???????????????????????????? ( )??710077???????????? ???????????????/?? : ??-??? ????????????????????????????????????????????????????????????????????????????E?E???E? ????????????-?-??????????????????????? ??????????????????????????????????E????????????????????????????????????????????????????????? ????????????????E??????????/???????????????????????!?????????????????/?????????????????? ???/?????????????????????????/??????E?E???????????*???E????????????????????????????????????????????????/???????????????????????? : ; ; ; ; ; ; ???????????????????????????????????????????????????????/??????E????????E? :::???*??????????????TP391. 4; TP317. 4A1001-3695( 2012) 12-4775-04????E????? doi: 10. 3969 / j. issn. 1001-3695. 2012. 12. 098 Frequency domain reciprocal-Gaussian cascade low-pass filtering denoising method of image WANG Jie??MAO Yu-quan??LI Si-jia??WU Chong-hu ( Information & Navigation Institute??Air Force Engineering University??Xi'an 710077??China) Abstract: To reduce the loss of details in the image frequency domain filtering??this paper proposed a new frequency method that reciprocal-Gaussian cascade low-pass filter. The method utilized the nature of reciprocal fast convergence and combined with Gaussian low-pass filter to achieve the joint filter of the image??it had significant impression on improving image quality by keeping a greater measure of image detail component while filtering the high-frequency noise??it processed the after image ha- ving higher contrast. Simulation shows that??comparing with traditional low-pass filter??reciprocal-ideal cascade low-pass fil- ter and reciprocal-Butterworth cascade low-pass filter based on the same effective filter area??the proposed method is the best on denoising effect. Key words: image denoising; frequency domain filtering; reciprocal filter; effective filter area; Gaussian low-pass filter; subjective evaluation method; objective evaluation method 0???? ??????????????????- ????????--??????????????????????????????????????????????? ??*?????????????????????????????????????????????????????????????E?E???E?E??????????????????????? ?????????????/???????????????/???????????/???????? ???????????????????????????????????????????????? ??E?E????????????????????????????????????????? ??????E?E???E??????????/??????????E?E????????????? ???? ????????????????????????????E????????????????????? ??1????2????3????4?? ??5??6??; ?????????????????????????????????????????E??????????? ??E??????????????????????????????????????????? ?????????????????????????????????????!???? ??????????????????????????????*/?????????????? ????????????????????????*/?/?????????????????/???? ????????E?????????????????????????????1 -??????????????????????????1????7????8?????????; ????; ???????????????????????/???????????????/?????????? ???/?????????????????/???????????????/???????? ?????????????????????????????????????????????????? ?????/???????????????????/???????????????????? ?????/????E?????????????????????????E???????E????? ???????????????????????????????????????????????? ???????/????????????????E?????????????????E????? ????E????????????????????????????????????????????? ????????????????E???????E????*???????????????????? ??9???1( b) ( c) ( discrete Fourier transform??DFT) ?1 ( b) ?????? ???????????? ?????????????????????*???? ????????E????*???? ?????????*????????E??????? ????????????E???????????E???????????????????????????E???????????E????????????? 1 ( c) ?---??E???????????E????? ??????????????E??????? ::????????????????2012-04-22;2012-05-28: ( 201102Y05 ) ; ???????????/?!??*?????????*?????????????????????*??????????? ( DYCX1040) ; ( 20110301)??????????????????????????*?????????????????????????????????????????*??????? : ( 1987-) ???????( xdwj061216 @ 126. com) ; ( 1957-) ??????????; ( 1987-) ????????; ( 1985-) ??????.*/???????????????????????/??????E???????????????????????????????????????? ???????????????????????/??????E???????????????????????????????????????????????/?/???????????????/??????E??? ?????????????????????????????????????????/??????E??????????????? ????????????????????????????????????????????????????????????????????????????????/??????E???????????????????????13????10??11??:??????????????????/????????????*???????E??????????????????????? ( )5 2 22- ??( u - M /2) + ( v - N /2) ??/ ( 2)?H( u??v) = e : ??M ?N ? ??????????????*????? ???????????? ??( ) :????E??????????????????????????????????????/?? ????E???????????????????7??a) :?????????????/ 1D( u??v) D?0H( u??v) =( 6)? 0( v) Du??D?0 ??7??8??b) : ?????????????????/ 1??7????????????????????????????????????H( u??v) =( 7)2n1 + ( 2 - 1) ??D( u??v) / D????0G( u??v) = F( u??v) H( u??v)( )1 2 2 ( u??v)??????: ( v) = Du??D????( u - M /2) + ( v - N /2) ?? 0?? ( M /2??N /2) ; ? ????????????????????????????????????????; n ; M N ????????????????????/???*?? ????????*??? E?????????2: G( u??v) ; F( u??v)?????????????????????????????????????? ; H ( u??v) ????????????????????????????????????????????? ????2. 1???????????????????????? ????2 ?????????E????????*??????????????????????????E??? ????????????????????????????E???????????????E????? ?????????????????????????????????*????????????????E? ????????E????????????????????????????????????????? ????????E?????????????*??/??????????????????????????????????????????????????????????*??????????????? ?????????????????????????????????????????????????? ?????????? ???? ???????????????????/????????????????????????????*? :---?????????????????????????? a) 3 ( a ) ???????????????????/?????????????????? ?? ???? 2( 8)S= D?0i b) ?????????????????/??????????????????E????????? /2u?v ??3 ( b) ?1 ?????????????????? ???????? ??????E????? ( 5) 1 /?????? 2?????? 222 - ??( u - M /2) + ( v - N /2) ??/ ( 2?) ( 9)H( u??v) = e = 1 /2?? 22d= ( u - M /2) + ( v - N /2) ?????????????????? ??g ?? 1. 1 ??????????*???22 d( 10)= 2?ln 2g ????12????2??8??( Fourier transform??FT) ???( DFT) ( inverse discrete fourier transform??IDFT) ??DFT IDFT ( 2 ) ( 3 ) ????????????????? ??????????????????????????????*????????????????????? ??????????*????????????????????????????????? ???????????????? ??????????????*??????? ?? ???????? ???????????????????????????????/???????????????? 22ln 2( 11)S= d= 2???g ??g c) ?????????????????????/???????????????????????? M - 1N - 13( c) ?( 7) /2????1 ?????/???? ???????????? ????- j2?( ux / M + vy / N)( 2)F( u??v) = f( x??y) e ? ? x = 0 y = 011M - 1N - 1=H( u??v) =( 12)12nj2?( ux / M + vy / N)f( x??y) =( 3)F( u??v) e? ? 1 + ( 2 - 1) ??D( u??v) / D?? 20????x = 0 y = 0MN D( u??v) = D???? ?????????????????????/????????????????0 2 2( 13)S= D( u??v) = D??0b : F( u??v) DFT ; f( x??y) ; M???????? ?????????*????????????d) ?????????????????/?????????????????????????????N ?? ??????????????????????????3 ( d) ?=??d?/???????????????????? ???????????????? d 1. 2 -???????????????????? 2 2 ??d ( u - M /2) + ( v - N /2) ???? ???????????????/??????d???????( 4) ??????? ????????E?????????E????????? ?????????????????????????/?????????????????????????????????????????????????????????????? ??????????????????E????????????????????????????????????????????????????? ( M /2??N /2) ????????*??????????? 2 2d = d= ( u - M /2) + ( v - N /2) d min??( 14) 2 2???2M N M N u - M /2 = a / ( v - N /2)1 u < + a / v - > - a / v - u ?? ? ? ?? ?2222( 4)H( u??v) = ?2f( v)= d??? ??????min0 else? 2 4 2f( v) = a/ ( v - N /2) + ( v - N /2) ( 15) : M N ; a ???? ??????????????????????????????????????????????( 15) ???????a ???/?? ?????!?????????/????E???2 5 f '( v) = - 4a/ ( v - N /2) + 2( v - N /2)( 16)??????????????????????????????????????E????????????? ???????????????????????????????!????????????????????62 f '( v) = 0??v = + N /2??f ( v ) ???? ?? 2a???? ?!??*??!?????? 4777??: -EE12 ?? ??????????????????????????????????????????E?E? 33 3 2 2 a??f( v) = d= ( 1 / 4 + )2?????????????????/??????????min?? ?? ???????? 333322 2 a2 )( 17)a= 1. 89?S= d= ( 1 / 4 +???? ??d d???? 2. 2 E?????E??? 4 D= 40??S= 1600?? = 48??a = 2. 5 * 10??n = 2; ?D?' = 2??D= 80??' = 2??= 96???????????????E??????!???????? ?? ????? ? ?????????????????/???*?! ?? ???????????? ??????????????????0 i o o ~?4( a1)E??????????? E??????????????????????????????? ( h3) ????? 2. 2. 1 ?/?????? 4( a1) ~ ( a3) ???4( b1) ~ ( b3) ????; 4( c1) ~ ( c3) ????; 4( d1) ~ ( d3) ??; 4( e1) ~ ( e3) ???????????4( f1) ~ ( h3) ??????-??E????????? ???????????????????????? ???????????????????????????????????????????/?????? ?????? ??????????????E????????????????? ??????????????E?E??????!?????????????????/???????? ???? ???????????????????????????????????? ???????????????????!?????????????????????????????? ???????????/???????????? ???????????????? ?????????????????????????????????????????????????? ???????????????? ???????????????????????? ???????????????????????????????????????????????????? ????????????????????E????????????????????????????? ???????????????????????????? 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