Wavelets on irregular point sets. (English) Zbl 0945.42019

Daubechies, Ingrid; Guskov, Igor; Schröder, Peter; Sweldens, Wim

Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 357, No. 1760, 2397-2413 (1999).

In this paper the authors review techniques for wavelet construction and analysis on one- and two-dimensional irregular grids. In the 1-D case, the usual subdivision scheme is introduced, and the Lemarié commutation formula is used to prove smoothness results. In the 2-D case the authors analyse progressive meshes. An equivalent commutation formula is reviewed together with a particular subdivision scheme, due to Guskov, based on minimizing certain second order difference functional. The analytic smoothness property of the resulting construction remains an open problem, but numerical evidence suggests that they are useful for practical applications.

Reviewer: Radu Balan (Princeton)

MSC:

42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60	Numerical methods for wavelets

Keywords:

multiresolution scheme; wavelets; irregular grid