Construction of Bases in Modules over Laurent Polynomial Rings and Applications to Box Spline Prewavelets
Abstract
We suggest a new method of basis construction for the kernel of a linear form on the Laurent polynomial module related to multivariate wavelets, and demonstrate its applications to box spline prewavelets, leading to small mask supports for C1 cubic and C2 quartic box splines in two variables, outperforming previously known constructions, and to trivariate piecewise linear prewavelets with at most 23 nozero mask coefficients.
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