Paper Info
Title
On cosine-modulated wavelet orthonormal bases.
Abstract
Multiplicity M, K-regular, orthonormal wavelet bases (that have implications in transform coding applications) have previously been constructed by several authors. The paper describes and parameterizes the cosine-modulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs, the scaling function uniquely determines the wavelets. This is in contrast to the general multiplicity M case, where one has to, for any given application, design the scaling function and the wavelets. Several design techniques for the design of K regular cosine-modulated WTFs are described and their relative merits discussed. Wavelets in K-regular WTFs may or may not be smooth, Since coding applications use WTFs with short length scaling and wavelet vectors (since long filters produce ringing artifacts, which is undesirable in, say, image coding), many smooth designs of K regular WTFs of short lengths are presented. In some cases, analytical formulas for the scaling and wavelet vectors are also given. In many applications, smoothness of the wavelets is more important than K regularity. The authors define smoothness of filter banks and WTFs using the concept of total variation and give several useful designs based on this smoothness criterion. Optimal design of cosine-modulated WTFs for signal representation is also described. All WTFs constructed in the paper are orthonormal bases.
Year
DOI
Venue
1995
10.1109/83.342190
IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Keywords
Field
DocType
multiplicity-m wavelet tight frames,signal representation,cosine-modulated wavelet orthonormal bases,scaling function,wavelet transforms,smooth designs,design techniques,transform coding,optimal design,short lengths,digital filters,wavelet vectors,transform coding applications,k-regularity,k-regular cosine-modulated wtf,filter banks
Digital filter,Filter bank,Artificial intelligence,Smoothness,Wavelet,Wavelet transform,Discrete mathematics,Ringing artifacts,Pattern recognition,Algorithm,Transform coding,Orthonormal basis,Mathematics
Journal
Volume
Issue
ISSN
4
2
1057-7149
Citations 
PageRank 
References 
16
1.81
15
Authors
2
Name
Order
Citations
PageRank
R. A. Gopinath141748.03
C. S. Burrus239175.14