JOURNAL BROWSE
Search
Advanced SearchSearch Tips
NEW LOOK AT THE CONSTRUCTIONS OF MULTIWAVELET FRAMES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
NEW LOOK AT THE CONSTRUCTIONS OF MULTIWAVELET FRAMES
Kim, Hong-Oh; Kim, Rae-Young; Lim, Jae-Kun;
  PDF(new window)
 Abstract
Using the fiberization technique of a shift-invariant space and the matrix characterization of the decomposition of a shift-invariant space of finite length into an orthogonal sum of singly generated shift-invariant spaces, we show that the main result in [13] can be interpreted as a statement about the length of a shift-invariant space, and give a more natural construction of multiwavelet frames from a frame multiresolution analysis of .
 Keywords
wavelet;frame;multiresolution analysis;shift-invariant space;
 Language
English
 Cited by
 References
1.
J. J. Benedetto and S. Li, The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal. 5 (1998), no. 4, 389-427. crossref(new window)

2.
J. J. Benedetto and O. M. Treiber, Wavelet frames: multiresolution analysis and extension principles, Wavelet transforms and time-frequency signal analysis, 3-36, Appl. Numer. Harmon. Anal., Birkhauser Boston, Boston, MA, 2001.

3.
C. de Boor, R. DeVore, and A. Ron, The structure of finitely generated shift-invariant spaces in L2($R^d$), J. Funct. Anal. 119 (1994), no. 1, 37-78. crossref(new window)

4.
M. Bownik, The structure of shift-invariant subspaces of $L^2(R^n$), J. Funct. Anal. 177 (2000), no. 2, 282-309. crossref(new window)

5.
H. Helson, Lectures on Invariant Subspaces, Academic Press, New York, 1964.

6.
R.-Q. Jia, Shift-invariant spaces and linear operator equations, Israel J. Math. 103 (1998), 259-288. crossref(new window)

7.
H. O. Kim, R. Y. Kim, and J. K. Lim, Local analysis of frame multiresolution analysis with a general dilation matrix, Bull. Austral. Math. Soc. 67 (2003), no. 2, 285-295. crossref(new window)

8.
H. O. Kim, R. Y. Kim, and J. K. Lim, Internal structure of the multiresolution analyses defined by the unitary extension principle, J. Approx. Theory 154 (2008), no. 2, 140-160. crossref(new window)

9.
H. O. Kim and J. K. Lim, On frame wavelets associated with frame multiresolution analysis, Appl. Comput. Harmon. Anal. 10 (2001), no. 1, 61-70. crossref(new window)

10.
H. O. Kim and J. K. Lim, Applications of shiff-invariant space theory to some problems of multiresolution analysis of $L^2(R^d)$, in: D. Deng, D. Huang, R.-Q. Jia, W. Lin and J. Wang (Eds.), Studies in Advanced Mathematics 25: Wavelet Analysis and Applications, American Mathematical Society/International Press, Boston 2001, 183-191.

11.
J. K. Lim, Gramian analysis of multivariate frame multiresolution analyses, Bull. Austral. Math. Soc. 66 (2002), no. 2, 291-300. crossref(new window)

12.
S. Mallat, Multiresolution approximations and wavelet orthonormal bases of $L^2$(R), Trans. Amer. Math. Soc. 315 (1989), no. 1, 69-87. crossref(new window)

13.
L. Mu, Z. Zhang, and P. Zhang, On the higher-dimensional wavelet frames, Appl. Comput. Harmon. Anal. 16 (2004), no. 1, 44-59. crossref(new window)

14.
A. Ron and Z. Shen, Frames and stable bases for shift-invariant subspaces of $L_{2}(R^{d})$, Canad. J. Math. 47 (1995), no. 5, 1051-1094. crossref(new window)

15.
A. Ron and Z. Shen, Affine systems in $L_{2}(R^{d})$: the analysis of the analysis operator, J. Funct. Anal. 148 (1997), no. 2, 408-447. crossref(new window)