Real solving for positive dimensional systems
Journal of Symbolic Computation
Dilation matrices for nonseparable bidimensional wavelets
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Numerically Computing Real Points on Algebraic Sets
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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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 the 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 (1992) into a polynomial problem and solve it using Grobner 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 16×16 filter bank, whose Sobolev exponent is 2.11, making this wavelet the most regular orthogonal linear-phase nonseparable wavelet to the authors' knowledge,