- 2001 (2) (entfernen)
- Part1: Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Scalar Fields; Part2: Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields (2001)
- 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.
- Wavelets Generated by Layer Potentials (2001)
- 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.