General Frame Multiresolution Analysis and Its Wavelet Frame Representation

Mang Ll  Hidemitsu OGAWA  Yukihiko YAMASHITA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.10   pp.1713-1721
Publication Date: 1996/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
multiresolution analysis,  general frame multiresolution analysis,  wavelet,  GFMRA wavelet frame,  generalized affine wavelet frame,  frame,  

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Summary: 
We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.