Abstract
Based on a concept for thresholding of wavelet coefficients, which was addressed in [8] and further explored in [6, 7], a method for balancing between non-threshold- and threshold shrinking of wavelet coefficients has emerged. Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by \(C^k\)-smooth basis functions. Global data fitting can be achieved with GERBS by fitting local functions to the data. One property of the GERBS construction is an intrinsic partitioning of the global data. Compression of the global data set can be achieved by applying the shrinking strategy to the GERBS local functions. In this initial study we investigate how this affects the resulting GERBS geometry.
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References
Bernstein, S.: Démonstration du théorème de weierstrass fondée sur le calcul des probabilités. Comm. Soc. Math. Kharkov 13, 1–2 (1913)
de Boor, C.: Splines as linear combinations of b-splines. A survey (1976)
Cohen, A., Daubechies, I., Feauveau, J.C.: Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. XLV, 485–560 (1992)
Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. XLI, 909–966 (1988)
Dechevsky, L.T., Bang, B., Lakså, A.: Generalized expo-rational b-splines. Int. J. Pure Appl. Math. 57(6), 833–872 (2009)
Dechevsky, L.T., Grip, N., Gundersen, J.: A new generation of wavelet shrinkage: adaptive strategies based on composition of Lorentz-type thresholding and Besov-type non-threshold shrinkage. In: Truchetet, F., Laligant, O. (eds.) Wavelet Applications in Industrial Processing V. Proceedings of SPIE,. Boston, MA, USA, vol. 6763, pp. 1–14 (2007)
Dechevsky, L.T., Gundersen, J., Grip, N.: Wavelet compression, data fitting and approximation based on adaptive composition of Lorentz-type thresholding and Besov-type non-threshold shrinkage. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 738–746. Springer, Heidelberg (2010)
Dechevsky, L.T., Ramsay, J.O., Penev, S.I.: Penalized wavelet estimation with besov regularity constraints. Math. Balkanica (N.S.) 13(3–4), 257–376 (1999)
Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 8(3), 425–455 (1994)
Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D.: Wavelet shrinkage: asymptopia? J. Roy. Stat. Soc. Ser. B 57(2), 301–369 (1995)
Eck, M., Hadenfeld, J.: Knot removal for b-spline curves. Comput. Aided Geom. Des. 12(3), 259–282 (1994)
Farin, G.: Curves and Surfaces for CAGD: A Practical Guide, 5th edn. Academic Press, New York (2002)
Lakså, A., Bang, B., Dechevsky, L.T.: Exploring expo-rational b-splines for curves and surfaces. In: Dæhlen, M., Mørken, K., Schumaker, L. (eds.) Mathematical Methods for Curves and Surfaces, pp. 253–262. Nashboro Press, Brentwood (2005)
Lyche, T., Mørken, K.: Knot removal for parametric b-spline curves and surfaces. Comput. Aided Geom. Des. 4(3), 217–230 (1987)
Schumaker, L.L., Stanley, S.S.: Shape-preserving knot removal. Comput. Aided Geom. Des. 13(9), 851–872 (1996)
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Bratlie, J., Dalmo, R., Bang, B. (2015). Wavelet Compression of Spline Coefficients. In: Dimov, I., Fidanova, S., Lirkov, I. (eds) Numerical Methods and Applications. NMA 2014. Lecture Notes in Computer Science(), vol 8962. Springer, Cham. https://doi.org/10.1007/978-3-319-15585-2_27
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DOI: https://doi.org/10.1007/978-3-319-15585-2_27
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