Wavelets bases defined over tetrahedra

• Autores: Liliana B. Boscardin, Liliana R. Castro, Silvia Mabel Castro, Armando De Giusti
• Localización: Journal of Computer Science and Technology, ISSN-e 1666-6038, Vol. 6, Nº. 1, 2006 (Ejemplar dedicado a: Seventeenth Issue), págs. 46-52
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper we define two wavelets bases over tetrahedra which are generated by a regular subdivision method. One of them is a basis based on vertices while the other one is a Haar-like basis that form an unconditional basis for Lp (T, Σ, μ), 1 < p < ∞, being μ the Lebesgue measure and Σ the σ - algebra of all tetrahedra generated from a tetrahedron T by the chosen subdivision method. In order to obtain more vanishing moments, the lifting scheme has been applied to both of them

• Referencias bibliográficas
  • References [1] J. Bey, “Tetrahedral Grid Refinement”, Computing, Vol. 55, No. 4, pp. 355-378, 1995.
  • [2] F. Dong and J. Shi, “Multiresolution Data Modeling for Irregular Data Fields based on Wavelets”, IEEE IV, 1997.
  • [3] M. Girardi and W. Sweldens, “A New Class of Unbalanced Haar Wavelets that form an Unconditional Basis for Lpon General Measure Spaces,...
  • [4] D. J. Holliday and G. M. Nielson, “Progressive volume Models for Rectilinear Data using Tetrahedral Coons Volumes”, http://prism.asu.esu/research/data/publications/paper00pvmnitv.pdf,...
  • [5] R. Lorentz and P. Oswald, “Multilevel Finite Riesz Basis for Sobolev Spaces”, Proc. of the 9th Int. Conference on Domain Decomposition...
  • [6] J. M. Lounsbery, Multiresolution Analysis for Surfaces of Arbitrary Topological Type, PhD. Thesis, University of Washington, Washington,...
  • [7] S. Muraki, “Approximation and Rendering of Volume Data using Wavelet Transforms”, Proc. of Visualization’92, pp. 21-28, 1992.
  • [8] G. M. Nielson, I. H. Jung and J. Sung, “Haar Wavelets over Triangular Domains with Applications to Multiresolution Models for Flow over...
  • [9] P. Schröder and W. Sweldens, “Spherical Wavelets: Efficiently Representing Functions on the Sphere”, ACM Proceedings of SIGGRAPH’95, pp....
  • [10] E. Stollnitz, T. DeRose and D. Salesin, Wavelets for Computer Graphics: Theory and Applications, Morgan & Kaufmann Publishers Inc.,...
  • [11] W, Sweldens, “The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions”, Proc. of the SPIE, vol. 2569, pp.68-79, 1995.
  • [12] W, Sweldens, “The Lifting Scheme:Custom-Design Construction of Biorthogonal Wavelets”, Appl. and Computational Harmonic Analysis, Vol.3,...