一种双正交多小波滤波器的设计及应用.pdf

1、41 3 2v(1 S) Vol.41null No. 32011 M5Journal of Henan University ( Natural Science) M ay 2011Blo ro !9#李永军1,徐晓蓉2,张彦波1,张东明1( 1.河南大学物理与电子学院河南开封 475001; null 2.湖南文理学院湖南 常德415000)null l : 2010null08null09nullTe: +( 1977- ), 3, 2 7 , V, =.Z_:Y_m) .Knull1: M icchelliXuy M“lo , 1_ u uW, f f ,y BF aalo ro ,i

2、 ro s E,KF ro m s k,iT s.1oM:lo;sOs;s; ms |:TP391null null nullDS : AcI|: 1003- 4978( 2011) 03- 0304- 04Design and Application of a Biorthogonal Multiwavelet FilterLI Yongnulljun1, XU Xiaonullrong2, ZHANG Yannullbo1, ZHANG Dongnullming1(1 . School of Physics and Electronics, H enan University, Kaif

3、eng H enan 475001, China;2. H unan University of Arts and Science, Changde H unan 415000, China)Abstract: On the basis of thetheory of invariant set multinullwavelets established by M icchelli and Xu, a biorthogonalmultinullwavelets filter is designed in this paper with many characteristics, such as

4、 symmetry, compact support andorthogonality. In this filter, the selfnullaffinetriangle domain is as support interval, and constant function is as scalingfunction. In this paper, the algorithms of decomposition and reconstruction of this filter and the test about thedecomposition and reconstruction

5、of iris imageare given, the experiment result is analyzed.Key words: biorthogonal multinullwavelets; reconstruction and decomposition; multinullresolution analysis; lrisnull nulla ah |) Es1,X L“ lo V ? H t,7lo V1 . Plo1Blo ,lo ?Z.lo/ZE2null3 , Charles A. MicchelliXU Yuenullshengy 1_ +M“lo4null6 , ro

6、 we7 2, K “,M ro H, “s,Tlos ? ,H r, HE H7 .lom) , ?z m +, B ? z+4 |ZE. MicchelliXuy M“lo , 1_ u uW, f f ,yBF aalo ro ,i ro s E,KF ro m s k,iT s, +4 | MY $.1 nulllo ro pl 1_ + unullnullnull = (x, y) | 0 null x null D, 0 null y null D, m1 U.4/ 4 l 1_ ri nullR2 null R2, i = 0, 1,2, 3,t V I unulls40 u,

7、nulli null=ri( null) , i = 0,1,2, 3, m2 U.r0 =12 00 12nullnull , null null null null null null null null r1 =12 00 12nullnull +D2D2, +,:Blo ro !9#305nullr2 =12 00 12nullnull +0D2, null null null null null r3 =- 12 00 - 12nullnull +D2D.nullm1null uWnull null null null null null null null null null nu

8、ll null null null nullm2 null null 40 unull null Fig.1 null Support Interval null null null null null null null null null null null Fig.2 null Four mapping sub regions of nulllnull(null, null) unullf ,null(null, null) null= 1A0nullnull(null,null), (1) A 0nullLebesgue, nullnull(null, null) +f , nulln

9、ull(null,null) = 1, null (null, null) null null,0, null otherwise.TL2null=Q V bW, V0nullfB bW, * V0 null L2 ( null).4g=f ,lL 0Ti(T ig)(null, null) null= g( r- 1i (null, null) nullnulli(null,null), i = 0,1, 2,3. (2)null null L 0Ti5 , VL 0=f g /B“ 3* bWVj+ 1 null Vj,Vj+ 1 = T0 Vj null T 1V j null T 2V

10、j null T 3V j. (3) V j null= spannullj, k nullK = kj nullk1 , ki null 0, 1,2,3, nullj , kf , l /5 :nullj, k(null,null) null= 2j( Tkj null Tkj-1 null nullnullT k1 null null(null, null) , (4) j ,2jSy ,“YV 0Tinull nullj, k. T(3),( 4) VBf bW:V1 = sp an null1, 0, null1, 1 , null1, 2 , null1, 3, (5) null1

11、, i, unulli null null f m2.V0 null V1,5 ,f VBf V U:null(null, null) = null3p= 0apnull1, p (null,null) null p = 0,1,2,3. (6)null null T(6)#f VZF:1A0nullnull(null,null) = 2a0 1A0nullnull 0(null, null) + 2a1 1A0nullnull1 (null, null) + 2a2 1A0nullnull2 (null, null) + 2a3 1A0nullnull3 (null, null),1 = a

12、20 + a21 + a22 + a23.(7)null nullZFBFap = a0, a1, a2, a3 = 12 , 12, 12 , 12 , (8) 1 pY ro .Vjlo0 bWW j bW bW5Vj+ 1 = Vj null Wj . (9)dim ( V0) = 1, dim( V1) = 4,5dim(W0) = 3.lW0 null= spannull1, null2 , null3 , nulli, i = 1,2, 3 unulllof , s f .W0 null V1 ,5lof Vf V U:nullr (null, null) = null3p= 0b

13、rpnull1, p (null, null), null i = 0,1,2,3. (10)306null 2v(1 S) ,2011 M,41 3 lb1p = b10, b11, b12, b13, b2p = b10, b11, b12, b13 , b3p = b10, b11, b12, b13 . lof l() V ZF:nullai, bjnull= 0, i = 1 null j = 1,2,3,nullbi, bjnull= 0, i null j null i, j = 1,2, 3,nullbi, bjnull= 0, i = j null i, j = 1,2, 3

14、.(11)Y ro , BF:b1p = b10, b11, b12, b13 = 12, - 12,0, 0,b2p = b20, b21, b22, b23 = 0, 0, 12, - 12,b3p = b30, b31, b32, b33 = 12 , 12, - 12 , - 12 .(12)2 nulllosOs T(12) lo S bWW0, 0Ti VB/j + 1lo bWW j+ 1:Wj+ 1 = T 0W j null T 1W j null T 2W j null T 3W j. (13) Blo bWW j null= spannullj, K nullK = kj

15、 nullk1, ki null 0,1,2,3, r = 1,2,3,lof nullj, K (null, null)l:nullj, K (null, null) null= 2j (T kj nullT kj- 1 null nullnull T k1 nullnullr (null, null) , r = 1, 2,3. (14)null nullB T(9) V bW5Vj = V0 null W0 null W1 null null null W j- 2 null Wj- 1, (15)“lo bW sPs.3 nulllosBf f null null, T ViHq, V

16、f V U8 :f j(null,null) = nullnullj , Knullj , K (null, null), (16)nullj, K f “ . T(14) , f VV U:f j (null, null) = nullnull(null, null) + null3r= 0 nullj- 1i= 0 nullKnullri, K nullri, K , (17) nullri, K lo“ . L=,+Y m) H,Y ro Y ro B F ro H 4null4 = (ap )T, (b1p )T , (b2p)T , (b3p) T T, (18)s H, T(18)

17、B ro T(17),5ms,sm s,K T(13)(15)Y ro TTssP qs.los E,H, V/M “s“ .sm, P ro s ro . H 5 , ro , ? LC .4 null kTs ro H 4null4m3s,m3 BBB144 null720 m9 .m3 ATB|v T(17)sT m4 U,m4 ATB|v T(17)s,T m5 U,“ m3BQlos. VnVBQs16 vsT, B vBlosY, Y mBZ_ s, P BY Y, Y. HMQ,5m5 ,T m6 U. +,:Blo ro !9#307nullm3null S mnull nul

18、l null null null null null null null null null null null null null null nullm4 nullsTnull Fig. 3null Original iris imagenull null null null null null null null null null null null null null Fig.4 null Image of line resolutionm5 nullBQs mnull null null null null null null null null null null null nul

19、l null nullm6 null mFig. 5null Iris image after first decomposition null null null null null null null null null null null Fig.6null Reconstructed iris imagem6 m3m, ?zm1 Amm Y.B (MsDIS KvMAXP V U mM, l /:DIS = null# Si= 1(p 1i - p2 i )2/# S, MAXP = max | p 1i - p2 i | .null null (MsV U m (Ms,7 KvV U

20、 m Msvl, l mBm.1 m6m3, DIS = 4. 1129e- 015 , MAX P = 2. 8422e-014,db4lom3s,mmDI S = 7.6353e- 012 , MAX P = 8. 7951e- 011.Vn (MsDIS KvMAX P1db4lol3 ), ro Tm+ I Y,i .5 null MicchelliXuy M“lo , 1_ u uW, f f ,yBF aalo ro , “s, ? ,H r. ro BQsBm16Z_+, m B qZ_/ A + H,loY v ? .yN ro ?z m , B z+4 |ZE. ID: 1

21、M orris M, Akunuri V. More results on orthogonal wavelets with optimum timenullfrequency resolution J/ Proc SPIE 2491,1995: 52- 62. 2 Alpert B. A class of bases in L2 for the sparerepresentation of integral operatorsJ. SIAM J. Math. Analysis, 1993,24. 3 Goodman TNT, Lee S L. Wavelet of multiplicity

22、J . Trans Amer Math Soc, 1994, 338(2): 639- 652. 4 MICCHELLICA, XU Y. Using thematrix refinement equation for theconstruction of wavelets on invariant sets number alnullgorithmJ. 1991: 75- 116. 5 MICCHELLI C A, XU Yuenullsheng. Reconstruction and decompositon algorithms for biorthogonal multiwavelet

23、s J .Multinulldimensional Systems and Signal Processing, 1997,8: 31- 69. 6 MICCHELLI C A, XU Y. A construction of refinable sets of interpolating wavelets J. Results in Mathematics, 1998, 3:59- 372. 7 Laws K I. Texture energy measuresCnullProc Image Understanding Workshop. Los Angeles, 1979:47- 51. 8 Prazenica R J, Lind R, Kurdila A J. Uncertainty estimation from volterra kernels for robust flutter analysis J . AIAA -2002- 1650,2002. 9, M d. MY &zkYJ.1,2002, 28(1): 1- 10.3 I :