A Study On Minimum-energy Vector-valued Wavelets Tight Frames

In this paper, minimum-energy vector-valued wavelet tight frames are introduced. It’s a important and meaningful work for us to study on wavelet tight frames, because they are able to maintain the advantages of orthogonal wavelet basis, and at the same time solve its deficiency such as contradiction among compact support, continuity and symmetry. As we know, there are some researches on wavelet frames and multi-wavelets tight frames, however, research on vector-valued wavelet tight frames is very little. In this paper, definition and concept of minimum-energy vector-valued wavelet tight frames are proposed based on the wavelet tight frames and the vector-valued wavelet and the conditions for scaling functions to generate a minimum-energy vector-valued wavelet tight frame. In addition, decomposition and construction algorithm is given out. In particular, a property of the minimum-energy vector-valued wavelet tight frames will be investigated by multiplied on the left side of the vector-valued scaling functions.