Digital filters associated with bivariate box spline wavelets

Wenjie He; Mingjun Lai

doi:10.1117/12.276850

1 October 1997 Digital filters associated with bivariate box spline wavelets

Wenjie He, Mingjun Lai

Author Affiliations +

Journal of Electronic Imaging, Vol. 6, Issue 4, (October 1997). https://doi.org/10.1117/12.276850

Abstract

Battle-Lemarié's wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to ∞. The passing and stopping bands of the ideal filter are dependent on the structure of the box spline function. Several possible ideal filters are shown. While these filters work for rectangularly sampled images, hexagonal box spline wavelets and filters are constructed to process hexagonally sampled images. The magnitude of the hexagonal filters converges to an ideal filter. Both convergences are shown to be exponentially fast. Finally, the computation and approximation of these filters are discussed.

Citation Download Citation

Wenjie He and Mingjun Lai "Digital filters associated with bivariate box spline wavelets," Journal of Electronic Imaging 6(4), (1 October 1997). https://doi.org/10.1117/12.276850

Published: 1 October 1997

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