Refine
Year of publication
- 2001 (2) (remove)
Document Type
- Preprint (2)
Language
- English (2)
Has Fulltext
- yes (2)
Keywords
- boundary-value problems of potent (1)
- limit and jump relations (1)
- multiscale analysis (1)
- potential operators (1)
- pyramid scheme (1)
- regular surface (1)
- wavelets (1)
Faculty / Organisational entity
Abstract: The basic concepts of selective multiscale reconstruction of functions on the sphere from error-affected data is outlined for scalar functions. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well-represented in terms of only a relatively small number of expansion coefficients at various resolution levels. A new pyramid scheme is presented to efficiently remove the noise at different scales using a priori statistical information.
By means of the limit and jump relations of classical potential theory the framework of a wavelet approach on a regular surface is established. The properties of a multiresolution analysis are verified, and a tree algorithm for fast computation is developed based on numerical integration. As applications of the wavelet approach some numerical examples are presented, including the zoom-in property as well as the detection of high frequency perturbations. At the end we discuss a fast multiscale representation of the solution of (exterior) Dirichlet's or Neumann's boundary-value problem corresponding to regular surfaces.