陽明大學(xué)放射醫(yī)學(xué)科學(xué)研究所(編輯修改稿)
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【文章內(nèi)容簡介】 ??????Implementation .for )2/( tol e a dsw hi c h ,...,0,1/ 22...,1, 1/a t x s i g na l t heS a m pl e jjZllfa jl ???????Zljlj )lx(a(x )f 2?? Step 1 : Approximate the original signal f by a step function of the form s i g na l . t heofdom a i n on t he de pe nds ra ng e:s i g na l . t heof fe a t ure s e s s e nt i a l t hec a pt ure e noug h t o s m a l l:lj( 4 . 5 ) 1( 4 . 4 ) (.f o r c o m p o n e n t s Wi t s i n t o )(2 De c o m p o s e2 S t e pjψ ( x ) ) / 2( x )()( 2 x( x ) ) / 2 x)( ψ( 2 x )jllxl??????????????( 4 . 7 ) 1( 4 . 6 ) (:Rx a l lf o r h o l d s r e l a t i o n s f o l l o wi n g T h ex 11111x ) ) / 2ψ ( 2x)(2()x(2x ) ) / 2(2 x)2( ψx)(2x2jjjjjjj????????????????? Example 1 0 02 , de c om pose f i nto W ,W ,V c om pon e nts .f ( x) 2 ( 4 ) 2 ( 4 1 ) ( 4 2) ( 4 3 )4 ( 2 2 4 1 2 ( 24 2 4( 1 / 2 ) ( 2( 1 / 2 ) 2( 1 / 2 ) 4 3 4( 1 / 2 1 ) ( 2jx x x x( x ) ( ψ x ) ( x ) ) / 2( x ) ( ( x ) ψ x ) ) / 2( x ) ( x ) ( ψ x ) ( x ) ) / 2( x ) ( x ) (? ? ? ?????? ? ?? ? ??? ? ? ? ? ? ???? ? ?? ? ? ? ? ? ?? ? ? ? ?111 0 0( 1 / 2 2( 1 / 2 ) f ( x) [ ( 2 2 ] [ 2 ( 2 ][ ( 2 1 2 1 ] / 2 [ 2 1 ( 2 1 ] / 2( 2 1 2 2W c om pon e nts : ( 2 1V c om pon e nts : 2 2V V ,Wf ( x) ( 2 1 (x) ψ ( x ) ) / 2ψ x ) ( x ) ( x ) ψ x)ψ x ) ( x ) ( x ) ψ x)ψ x ) ( x )ψ x)( x )ψ x) ψ x ) ( x )???????? ? ?? ? ? ?? ? ? ? ? ? ? ?? ? ???? ? ? ?General deposition scheme 111122112211121121111111111222222222 222( 4 . 1 1 ) 22(122( 4 . 1 0 ) 22(222222( 4 . 7 ) 1 ( 4 . 6 ) (( 4 . 9 ) 12222: t e r m sodd a n de v e n i n t o 2 s u m t h eDi v i d e : 1 S t e p??????????????????????????????????????????????????????????????????????????jjZkjkkjkkjZkjkjZkjkjjjjjjjjjjjjjjjZkjkZkjkjkjkjfw)kx()aa()kx(ψ)aa(/))kx(ψ)kx((a/))kx()kx(ψ(a( x )f/))kx(ψk)x2()kx(/))kx(k)x2ψ()kx()kx(kxx ) ) / 2ψ ( 2x)(2()( 2 xx ) ) / 2(2 x)2( ψx)(2)kx(a)kx(a( x )f)kx(a( x )f??????????????Wj1ponent Vj1ponent ? Theorem (Haar Deposition) 2 2 22 wh e r e as d e c o m p o s e d bec a n T h e n V 2002122111122112211111111111jf. ..fwwfwfaaaaabw i t hV)kx(afW)kx(ψbw,fwff)kx(a( x )fjjjjjjjjjkjkjkjkjkjkZkjjjkjZkjjjkjjjjjZkjjkj??????????????????????????????????????????????????????????? Example ????????????1208888880018221202.c o m p o n e n t s V,W, Wi n t o f d e c o m p o s e 1,x0 813, F i g u r ekkk)()/kf()x(fk),/kf(a,j?V8ponent V7ponent V6ponent V4ponent W7ponent Reconstruction jjjlZljjl39。jk39。jk39。j39。j/)l(x/laf)lx(af ( x )b.bWW39。212 i n t e r v a l t h eo v e r h e i g h t off u n c t i o n s t e p a is d o n e , is t h i sO n c e2 r e b u i l d toa l g o r i t h mt i o n r e c o n s t r u c a n e e d m o d i f i e d ,b e e n h a v e l a r g e r k e e po n l y o u t , t h r o wn bec a n s m a l l a r e t h a t c o m p o n e n t s T h e :n c o m p r e s s i o D a t a o u t . t h r o wn bec a n sf r e q u e n c i e u n w a n t e d t h e t oi n gc o r r e s p o n d c o m p o n e n t s T h e : f i l t e r i n g N o i s e? t h e n w h a tj,j39。0f o r c o m p o n e n t s Wa n dV i n t o f d e c o m p o s e d H a v i n gj0????????????????General reconstruction scheme jlljjlklllklZkkllja)lx(a)x(fj 1l 0W)kx(ψbwV)kx(a)x(fw h e r eWww)x(w)x(ff ( x ) c o n s t a n t s ofn c o m p u t a t i o f o r t h e a l g o r i t h m a f i n da n d 2 r e wr i t e To: Go a lf o r 2 a n d ( x )000100?????????????????????????General reconstruction scheme ????????????????????????????????????odd is 1 if e v e n is if ? ( 4 . 1 6 ) )2(?)( so ))122()22(( )()(h a v e we,by r e p l a c e d wi t h 4 . 1 2 U s i n g( 4 . 1 5 ) 1222( 4 . 1 4 ) 1222( 4 . 1 3 )
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