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Recursive Filtering for Splines on Hexagonal Lattices

D. Van De Ville, T. Blu, M. Unser

Proceedings of the Twenty-Eighth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'03), Hong Kong SAR, People's Republic of China, April 6-10, 2003, vol. III, pp. 301-304.



Hex-splines are a novel family of bivariate splines, which are well suited to handle hexagonally sampled data. Similar to classical 1D B-splines, the spline coefficients need to be computed by a prefilter. Unfortunately, the elegant implementation of this prefilter by causal and anti-causal recursive filtering is not applicable for the (non-separable) hex-splines. Therefore, in this paper we introduce a novel approach from the viewpoint of approximation theory. We propose three different recursive filters and optimize their parameters such that a desired order of approximation is obtained. The results for third and fourth order hex-splines are discussed. Although the proposed solutions provide only quasi-interpolation, they tend to be very close to the interpolation prefilter.


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