The Information Fusion Method Based on a Sort of Multiple Pseudoframes with Arbitrary Real Translation Constant

Chen, Qing Jiang; Chang, Miao

doi:10.4028/www.scientific.net/AMR.171-172.109

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HomeAdvanced Materials ResearchEngineering Materials, Energy, Management and...The Information Fusion Method Based on a Sort of...

The Information Fusion Method Based on a Sort of Multiple Pseudoframes with Arbitrary Real Translation Constant

Abstract:

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with real number translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.

Info:

Periodical:

Advanced Materials Research (Volumes 171-172)

Main Theme:

Engineering Materials, Energy, Management and Control

Edited by:

Zhihua Xu, Gang Shen and Sally Lin

Pages:

109-112

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.171-172.109

Citation:

Q. J. Chen and M. Chang, "The Information Fusion Method Based on a Sort of Multiple Pseudoframes with Arbitrary Real Translation Constant", Advanced Materials Research, Vols. 171-172, pp. 109-112, 2011

Online since:

December 2010

Authors:

Qing Jiang Chen, Miao Chang

Keywords:

Affine Fames, Biorthogonal Basis, Filter Function, Multiple Subspace Pseudofames, Real Number Translation, Time-Frequency Analysis Method

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References

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

DOI: https://doi.org/10.1090/s0002-9947-1952-0047179-6

[2] P. G. Casazza: The art of frame theory, Taiwanese Journal , of mathe-matics, Vol. 4, No. 2, pp.129-201. (2000).

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

[4] I. Daubechies: Ten Lectures on Wavelets. SIAM: Philadelphia. (1992).

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

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

[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).

Paper TitlePages

The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions

Authors: Yu Min Yu

Abstract: Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

926

The Character of Multiple Affine Pseudoframes with Filter Banks Based on a Pyramid Decomposition Scheme

Authors: Tong Qi Zhang

Abstract: In recent years, frames have been the focus of active research, both in theory and applications. In this paper, the notion of multiple affine pseudoframes for subspaces of space is introduced. The concept of a generalized multiresolution structure(GMRS) is proposed. The sufficient condition for the existence of a class of multiple pseudoframes with filter banks is obtained by virtue of a generalized multiresolution structure. An approach for constructing one GMRS of Paley-Wiener subspaces of is presented based on the pyramid decomposition scheme The characteristics of affine pseudoframes for subspaces of space is provided.

1111

The Research of Bivariate Pseudoframes of Subspace Based on a Pyramid Decomposition Scheme

Authors: Zong Ling An, Yong Mei Niu

Abstract: The notion of a generalized multiresolution structure and the concept of subspace bivariate affine pseudoframes are introduced. The pyramid decomposition scheme of a generalized multiresolution structure(GMRS) is established, which is generalization of Mallat's pyramid algorit- -hm. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented. Moreover, affine bivariate pseudoframe expansions of are constructed by virtue of the pyramid decomposition scheme.

1117

The Research of Multiple Subspace Pseudoframes with Integer Translation

Authors: Jin Chang Shi, Shui Wang Guo

Abstract: Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The construction of a GMS of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.

1129

Study of Trivariate Pseudoframes and Subspace Frames and their Applications in Solid-State Physics

Authors: Zhong Yin Chen, Qing Jiang Chen

Abstract: Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the trivariate generalized multiresolut- ion structure (TGMS) of subspace is proposed. The characteristics of trivariate affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

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