The Research of Trivariate Normalized Tight Frames and Pseudoframes of Subspace Based on a Pyramid Decomposition Scheme

Shi Heng Wang

doi:10.4028/www.scientific.net/AMR.721.733

Paper Titles

Application and Numerical Simulation of Advanced Small Pipes Grouting in Tunnel Engineering
p.706

Seismic Performance Analysis of Oil Pipeline with Crack Defects
p.710

Application of Steel Plates on the Retrofitting of Current Reinforced Concrete Coupling Beams
p.714

Axial Bearing Capacity of Steel Reinforced Concrete Short Column with Double Circular Steel Tubes
p.720

Propagation Characteristics of Coupled Wave through Micropolar Fluid Interlayer in Micropolar Elastic Solid
p.729

The Research of Trivariate Normalized Tight Frames and Pseudoframes of Subspace Based on a Pyramid Decomposition Scheme
p.733

The Stability and Perturbation of Bivariate Gabor Frames and Applications in Material Engineering
p.737

The Characteristics of Orthogonal Wavelet Frames and Canonical Frames and Applications in Material Science
p.741

On the Mechanism of Inter-Organizational Knowledge Creation in the Knowledge Network from the Perspective of Nonlinear Interaction
p.745

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 721The Research of Trivariate Normalized Tight Frames...

The Research of Trivariate Normalized Tight Frames and Pseudoframes of Subspace Based on a Pyramid Decomposition Scheme

Abstract:

The notion of trivariate normalized tight frames and a generalized multiresolution struc-ture and the concept of subspace trivariate affine pseudoframes are introduced. The pyramid decom-position scheme of a generalized multiresolution structure (GMRS) is established, which is generaliz-ation of Mallat's pyramid algorithm. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented. Moreover, affine trivariate pseudo frame expansions of are constructed by virtue of the pyramid decomposition scheme.

You might also be interested in these eBooks

Recent Advancement on Material Science and Manufacturing Technologies

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 721)

Pages:

733-736

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.721.733

Citation:

Cite this paper

Online since:

July 2013

Authors:

Shi Heng Wang

Keywords:

Biorthogonal Bases, Dual Pseudoframes, Filter Functions, Frames, Pyramid Decomposition Scheme, Subspace Frames, Trivariate, Wavelet Frame

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] D. Gabor, Theory of communication: J. Inst. Elec. Engrg., Vol. 93, pp.429-457, (1946).

Google Scholar

[2] R. J. Duffin, A. C. Schaeffer: A class of nonharmonic Fourier series , Trans. Amer. Math. Soc., Vol. 72, pp.341-366,(1952).

DOI: 10.1090/s0002-9947-1952-0047179-6

Google Scholar

[3] I. Daubechies, A. Grossmann, A. Meyer: Painless nonorthogonal expansions. J. Math. Phys.Vol 27, pp.1271-1283,( 1986).

DOI: 10.1063/1.527388

Google Scholar

[4] A.Ron, Z. Shen: Affine systems in L^2(R^d). (II) Dual systems. J. Fourier Anal. Appl. Vol 4, pp.617-637,( 1997).

Google Scholar

[5] S. Li, M. Ogawa: Pseudoframes for Subspaces with Applications. J. FourierAnal.Appl. Vol 10, pp.409-431,(2004).

Google Scholar

[6] S. Li: A Theory of Geeneralized Multiresolution Structure and Pseudoframes of Translates. J. Fourier Anal. Appl. Vol 6(1), pp.23-40, (2001).

Google Scholar

[7] J. J. Benedetto, S. Li: The theory of multiresolution analysis frames and applications to filter banks.Appl. comput. Harmon.Anal.vol5, pp.389-427,( 1998). 4

Google Scholar