Symmetric nearly shift-invariant tight frame wavelets

Authors:
A.F. Abdelnour;I.W. Selesnick
Affiliations:
Memorial Sloan-Kettering Cancer Center, New York, NY, USA;-
Venue:
IEEE Transactions on Signal Processing
Year:
2005

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Abstract

K-regular two-band orthogonal filterbanks have been applied to image processing. Such filters can be extended into a case of downsampling by two and more than two filters provided that they satisfy a set of conditions. Such a setup allows for more degrees of freedom but also at the cost of higher redundancy. The latter depends directly on the number of the wavelet filters involved. Tight frame filters allow the design of smooth scaling functions and wavelets with a limited number of coefficients. Moreover, such filters are nearly shift invariant, a desirable feature in many applications. We explore a family of symmetric tight frame finite impulse response (FIR) filters characterized by the relations H3(z)=H0(-z) and H2(z)=H1(-z). They are simple to design and exhibit a degree of near orthogonality, in addition to near shift invariance. Both properties are desirable for noise removal purposes.