Subspace affine pseudoframes with a generalized multiresolution structure and the pyramid decomposition scheme

Author

Song, Suluo ; Wang, Man

Author_Institution

Dept. of Appl. Math., Nanyang Inst. of Technol., Nanyang, China

fYear

2010

fDate

16-18 April 2010

Firstpage

25

Lastpage

29

Abstract

The rise of frame theory in applied mathematics is due to the flexibility and redundancy of frames. In this work, the notion of a generalized multiresolution structure of L2(R) is proposed. The definition of multiple pseudoframes for subspaces of L2(R) is given. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is derived based on such a generalized multiresolution structure. The pyramid decomposition scheme is also obtained.

Keywords

Fourier series; mathematical analysis; stochastic processes; Paley-Wiener subspaces; frame theory; generalized multiresolution structure; pyramid decomposition scheme; subspace affine Pseudoframes; Data compression; Filter bank; Focusing; Fourier transforms; Image processing; Image sampling; Mathematics; Signal processing; Signal resolution; Sufficient conditions; filter banks; generalized multiresolution structure; pseudoframes; pyramid decomposition scheme; univariate;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Management and Engineering (ICIME), 2010 The 2nd IEEE International Conference on

Conference_Location

Chengdu

Print_ISBN

978-1-4244-5263-7

Electronic_ISBN

978-1-4244-5265-1

Type

conf

DOI

10.1109/ICIME.2010.5477499

Filename

5477499