The Research of Orthogonal Symmetric Matrix-Valued Wavelets Packets with Multiscale and Applications

Abstract

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we introduce orthogonal matrix-valued wavelets with poly-scale, which are wavelets for vector fields, based on the notion of full rank subdivision operators. It is demonstrated that, like in the scalar and multiwavelet case, the existence of an orthogonal matrix-valued scaling function guarantees the existence of orthogonal matrix-valued wavelet functions. Secondly, we propose a construction algorim for compactly supported orthog onal two-directional matrix-valued wavelet packets. Lastly, A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is presented by means of matrix theory.