陽(yáng)明大學(xué)放射醫(yī)學(xué)科學(xué)研究所(2)(編輯修改稿)
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【文章內(nèi)容簡(jiǎn)介】 )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 ) 122( 4 . 1 2 ) 122001100000112kla2klaaw h e r elxaxfkxakxakxaxfx kx)x(x)(x)ψ()x(x)(x)()x(x)(ψ ( x ))x(x)(( x )kklZklZkkkZkkjjjjjj??????????????????????????????????????????????odd is 1 if e v e n is if ?? ))( ( )2()()(odd is 1 if e v e n is if ? ( 4 . 1 7 ) )2(?)(as wr i t t e n bec a n )( ,0000111110000110002klba2klbabaaw h e r exflxaxwxf2klb2klbbw h e r elxbxwkxψawS i mi l a r l ykkkklllZllkklZllkk??m a n n e r . r e c u r s i v e ai n on so a n dt s ,c o e f f i c i e n t h ed e t e r m i n e tsc o e f f i c i e n,t s .c o e f f i c i e n t h ed e t e r m i n e tsc o e f f i c i e n,odd is 1 if, e v e n is if, ) ( )2()()()(s u m t h e t o)2( A d d211100111122221011llllllkkkklZllokkabaaba2klba2klbaaw h e r eflxaxwxwxfkxψbw????????????????????????? Theorem (Haar Reconstruction) ?????????????????????????????????????????odd is 1 if, e v e n is if, a l g o r i t h m b y t h e j, u n t i lon so a n d 2,t h e n 1,f o r y r e c u r s i v e l d e t e r m i n e d a r e t h e 2 f o r 2 a n d 11110001002klba2klbaa39。j39。j39。jaw h e r eV)lx(a)x(fT h e n.j39。j 0W)kx(ψb)x(wV)kx(a)x(fw i t hwwffS u p p o s e39。jk39。jk39。jk39。jk39。jl39。jlZljjjlZk39。j39。j39。jk39。jZkkj??? Example s i g n a l . t t h er e c o n s t r u ct h e n n ) ,c o m p r e s s i o ( 8 0 % z e r o t oe q u a l 80%s m a l l e s t s e t t h e s i z e ,by t h eo r d e r i n gAf t e r .70f o r )2()( a n d )( wi t h120),2/( 1,x0 ,819, F i g u r e39。39。39。39。39。00072100888jkZkjjjkj0kbjWkxbxwV( x )axfwffkkfaj???????????????????????????80% pression 90% pression sample signal Filters and Diagrams 1kkkk1kkkkx21x21x)(L ( x )x21x21x)(hH ( x )xx a n d L ( x )hH ( x ) :hh?????????????????????????????????????????????? t h u sa r e s e q u e n c e s r e s u l t i n g T h e. t h e n ,}{x If)021 210( ),021 210(: a n d s e q u e n c e s t h ea r ew h i c h r e s p o n s e s , i m p u l s e t h e i r v i a L a n d H o p e r a t o r s )on ( c o n v o l u t i f i l t e r s D i s c r e t e2k?k=1,0 ?k=1,0 ? Deposition algorithm ?????????????1012211221][2 2njjkjkjkjkjkjkjkjkzyz*yaaaaab d e n o t e d n g ,d o w n s a m p l i c a l l e d is s e q u e n c e ai n tsc o e f f i c i e n odd t h ed i s c a r d i n g ofo p e r a t i o n T h i s a n d t h e n ,s u b s c r i p t se v e n o n l y k e e p weIf22222222.x21x21x)(L ( x )x21x21x)(hH ( x )1kkkk1kkkk ????????? ?4 .1 2 ) T h e o r e m 2 2(.)( a n d )( jj39。0f o r c o m p o n e n t s a n d i n
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