Poly-Scale Refinable Function and Their Properties

YANG Shou-zhi

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(12): 1477-1485

YANG Shou-zhi. Poly-Scale Refinable Function and Their Properties[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1477-1485.

Citation:

YANG Shou-zhi. Poly-Scale Refinable Function and Their Properties[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1477-1485.

Citation:

YANG Shou-zhi. Poly-Scale Refinable Function and Their Properties[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1477-1485.

PDF( 357 KB)

Poly-Scale Refinable Function and Their Properties

YANG Shou-zhi

Department of Mathematics, Shantou University, Shantou, Guangdong 515063, P. R. China

Received Date: 2004-11-16
Rev Recd Date: 2006-08-18
Publish Date: 2006-12-15

Abstract

Abstract

Poly-scale refinable function with dilation factor a was introduced. The existence of solutions of poly-scale refinable equation was investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function phi of a poly-scale refinable equation with integer dilation factor a were established. Some properties of poly-scale refinable function were discussed. Several examples illustrating how to use the method to construct poly-scale refinable function were given.
- poly-scale function,
- dilation factor,
- poly-scale refinable equation

FullText(HTML)

References(14)

References

[1]	Daubechies I.Orthonormal bases of compactly supported wavelets[J].Comm Pure Appl Math,1988,41(7):909—996. doi: 10.1002/cpa.3160410705
[2]	Daubechies I,Lagarias J C.Two-scale difference equations Ⅰ—Existence and global regularity of solutions[J].SIAM J Math Anal,1991,22(5):1388—1410. doi: 10.1137/0522089
[3]	Chui C K,LIAN Jian-ao.A study on orthonormal multiwavelets[J].J Appl Numer Math,1996,20(3):273—298. doi: 10.1016/0168-9274(95)00111-5
[4]	Lian J.Orthogonal criteria for multiscaling functions[J].Appl Comput Harmon Anal,1998,5(3):277—311. doi: 10.1006/acha.1997.0233
[5]	YANG Shou-zhi,CHENG Zheng-xing,WANG Hong-yong.Construction of biorthogonal multiwavelets[J].J Math Anal Appl, 2002,276(1):1—12. doi: 10.1016/S0022-247X(02)00240-8
[6]	YANG Shou-zhi.A fast algorithm for constructing orthogonal multiwavelets[J].ANZIAM Journal,2004,46(2):185—202. doi: 10.1017/S144618110001378X
[7]	Cabrelli A C,Gordillo M L. Existence of multiwavelets in Rn[J].Proc Amer Math Soc,2002,130(5):1413—1424. doi: 10.1090/S0002-9939-01-06223-2
[8]	Dyn N,Levin D.Subdivision schemes in geometric modelling[J].Acta Numer,2002,11(1):73—144. doi: 10.1017/CBO9780511550140.002
[9]	Cohen A,Dyn N,Matei B.Quasilinear subdivision schemes with applications to ENO interpolation[J].Appl Comput Harmon Anal,2003,15(2):89—116. doi: 10.1016/S1063-5203(03)00061-7
[10]	Dekel S, Leviatan D. Wavelet decompositions of nonrefinable shift invariant spaces[J].Appl Comput Harmon Anal,2002,12(2):230—258. doi: 10.1006/acha.2001.0373
[11]	Blu T,Thvenaz P,Unser M.MOMS: Maximal-order interpolation of minimal support[J].IEEE Trans Image Process,2001,10(7):1069—1080.
[12]	Dekel S,Dyn N.Poly-scale refinablity and subdivision[J].Appl Comput Harmon Anal,2002,13(1):35—62. doi: 10.1016/S1063-5203(02)00006-4
[13]	YANG Shou-zhi,YANG Xiao-zhong.Computation of the support of multiscaling functions[J].Chinese J Numer Math Appl,2005,27(2):1—8.
[14]	PENG Li-zhong,WANG Yong-ge.Parameterization and algebraic structure of 3-band orthogonal wavelet systems[J].Sci China Ser A,2001,44(12):1531—1543. doi: 10.1007/BF02880793