Title :
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
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;
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
DOI :
10.1109/ICIME.2010.5477499
