'Konstruktion af tight multiwaveletframes'

Student thesis: Master thesis (including HD thesis)

  • Linda Østervig Jensen
  • Helene Pilgaard Larsen
  • Hanne Lyngby Laursen
4. term, Mathematics, Master (Master Programme)
'In this thesis we discuss the construction of tight multiwavelet frames for $L^2(\R)$ based on frame multiresolution analysis. The setup is inspired by the construction of orthonormal wavelet bases for $L^2(\R)$ via classic multiresolution analysis. We describe selected properties of frames with the intention to construct multiwavelet frames for $L^2(\R)$. We set up a frame multiresolution analysis which gives a systematic way to construct waveletframes for $L^2(\R)$. Wavelet frames constructed via frame multiresolution analysis are attractive from a computational aspect. We discuss two principles for constructing tight multiwavelet frames, which both integrate the frame multiresolution idea: The unitary extension principle and the oblique extension principle. Therefore tight multiwavelet frames constructed via these two extension principles keep the computational advantages from multiresolution analysis. We prove the two extension principles. Tight multiwavelet frames constructed via the unitary extension principle have some restrictions. One of these restrictions is related to the approximation order provided by the tight multiwavelet frame. We demonstrate that the tight multiwavelet frames constructed via the oblique extension principle can have a larger approximation order than the ones constructed via the unitary extension principle. Finally we illustrate the advantages concerning approximation order gained by the oblique extension principle in relation to the unitary extension principle in an example based on $B$-splines.'
Publication dateJun 2006
ID: 61068227