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Journal Articles IEEE Transactions on Signal Processing Year : 1998

Design of regular nonseparable bidimensional wavelets using Grobner basis techniques

Abstract

The design of two-dimensional (2-D) filter banks yielding orthogonality and linear-phase filters and generating regular wavelet bases is a difficult task involving algebraic properties of multivariate polynomials. Using cascade forms implies dealing with nonlinear optimization. We turn the issue of optimizing the orthogonal linear-phase cascade from Kovacevic and Vetterli into a polynomial problem and solve it using Gr¨obner basis techniques and computer algebra. This leads to a complete description of maximally flat wavelets among the orthogonal linear-phase family proposed by Kovacevic and Vetterli. We obtain up to five degrees of flatness for a 16 x 16 filter bank, whose Sobolev exponent is 2.11, making this wavelet the most regular orthogonal linearphase nonseparable wavelet to the authors' knowledge.
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inria-00098579 , version 1 (25-09-2006)

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Jean-Charles Faugère, Francois Moreau de Saint Martin, Fabrice Rouillier. Design of regular nonseparable bidimensional wavelets using Grobner basis techniques. IEEE Transactions on Signal Processing, 1998, 46 (4), pp.845-856. ⟨10.1109/78.668541⟩. ⟨inria-00098579⟩
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