Theory of Regular M-band Wavelet Bases

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Title: Theory of Regular M-band Wavelet Bases
Author: Steffen, P.; Heller, Peter Niels; Gopinath, Ramesh A.; Burrus, C. Sidney
Type: Journal article
Keywords: K-regular; M-band; orthonormal wavelet bases; image coding
Citation: P. Steffen, P. N. Heller, R. A. Gopinath and C. S. Burrus, "Theory of Regular M-band Wavelet Bases," IEEE Transactions on Signal Processing, 1993.
Abstract: This paper constructs K-regular M-band orthonormal wavelet bases. K-regularity of the wavelet basis is known to be useful in numerical analysis applications and in image coding using wavelet techniques. Several characterizations of K-regularity and their importance are described. An explicit formula is obtained for all minimal length M-band scaling filters. A new state-space approach to constructing the wavelet filters from the scaling filters is also described. When M-band wavelets are constructed from unitary filter banks they give rise to wavelet tight frames in general (not orthonormal bases). Conditions on the scaling filter so that the wavelet bases obtained from it is orthonormal is also described.
Date Published: 1993-12-20

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