A Study On The Characteristics Of Minimum-energy Vector-valued Wavelets Tight Frames With Dilation Factor M

Minimum-energy vector-valued wavelet tight frames with dilation factor M are introduced in this paper. Wavelet tight frames not only maintain the advantages of orthogonal wavelet basis and bi-orthogonal wavelet basis, but also solve their deficiency. The studies on wavelet tight frames which are produced by several scaling functions are rare. More and more people study on this subject. Vector-valued wavelets are used widely in many fields of science. So I made a research on the minimum-energy vector-valued wavelet tight frames in this paper. This paper gives the concept and equivalent propositions of minimum-energy vector-valued wavelet tight frames with dilation factor M. Those give a method of constructing minimum-energy vector-valued wavelet tight frames with dilation factor M. Besides, I give an existence criterion of minimum-energy vector-valued wavelet tight frames with dilation factor M. That gives the theory basis of constructing minimum-energy vector-valued wavelet tight frames with dilation factor M. In order to offer the theory basis of constructing many minimum-energy vector-valued wavelet tight frames with dilation factor M, I study on how to generate new minimum-energy vector-valued wavelet tight frames with dilation factor M by orthogonal matrixes. We can use a rotation matrix to replace the orthogonal matrix in this paper. Many different orthogonal matrixes can be got through changing the rotation angles (a two-dimensional rotation matrix is decided by one rotation angle, and a three-dimensional rotation matrix is decided by three rotation angles). We can get higher dimensional rotation matrixes from two-dimensional and three-dimensional rotation matrixes by the method of constructing orthogonal matrixes, solving the problem of constructing many orthogonal matrixes. Finally, I give examples of using two-dimensional and three-dimensional rotation matrixes to generate new minimum-energy vector-valued wavelet tight frames with dilation factor M...