MRA-Based Multi-Wavelet Frames And Matrix-Valued Frames

The property of redundancy makes constructions of wavelet frame systems more easier. And it also guarantee the robustness of reconstruction. The structures of a multiresolution analysis are associated with fast decomposition and reconstruction algorithms. Due to the unitary extension principle, the strong point of frame and multiresolution analysis are combined. It also makes constructing wavelet frame painless.This paper studies the basic theory of wavelet tight frame. We proved the unitary extension principle of multi-wavelet frames, and discussed the existence of such frames. And approximation properties and symmetric properties are also involved, as well as a way in constructing frames called parameterization. Further, we studied basic properties of matrix frame and proved the extension principle.