Parameterizations of masks for 3-band tight wavelet frames by symmetric extension of polyphase matrix

This paper deals with the construction of 3-band tight wavelet frames with symmetric properties using symmetric extension and parameterizations of the paraunitary matrix. Firstly, we construct a paraunitary matrix which is a symmetric extension of polyphase matrix corresponding to compactly supporte...

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Bibliographic Details
Published in:Applied mathematics and computation 2013-12, Vol.225, p.461-474
Main Authors: Sun, Jianjun, Huang, Yan, Sun, Shuyao, Cui, Lihong
Format: Article
Language:English
Subjects:
3-Bands
Construction
Frames
Masks
Mathematical models
Parameterizations
Parametrization
Paraunitariness
Polyphase matrix
Smoothness
Symmetric extension
Variability
Wavelet
Wavelet frames
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Summary:This paper deals with the construction of 3-band tight wavelet frames with symmetric properties using symmetric extension and parameterizations of the paraunitary matrix. Firstly, we construct a paraunitary matrix which is a symmetric extension of polyphase matrix corresponding to compactly supported wavelet frames with the least number generators. Further, we present symmetric characters and uniformity of wavelet frames with different filter lengths in terms of paraunitary matrix. Then, we focus on investigating the parameterizations of masks for 3-band tight wavelet frames with 3N filter length. Finally, examples of 3-band wavelet frames with good smoothness are constructed based on the parameterizations of masks.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.09.065