| In recent years,wavelet transform has become a practical analysis tool in signal processing,and wavelet theory has been well developed.With the deepening of the study of wavetheoretical research,scholars have shifted from single wavelet research to multiwavelet research.Multiwavelet maintains many aspects of single wavelet advantages,and overcome the shortcomings of single wavelets.At present,the construction of multiwavelets is still one of the frontier topics of wavelet theory research.In the study of high-order balancedmultiscale functions,Li Youfa proposed Para-unitary two-Scale similar transformation(PTST),a corresponding display construction example is given.And Yang Shouzhi also put forward the concept of two-way wavelet with the help of the method of studying the construction of multiwavelet theory,which further promoted the development of two-way wavelet.In this paper,we mainly studies the construction of Armlet multiwavelet,the properties of two-dimensional four-way matrices valued wavelet and construction algorithm.The main contents are as follows:In chapter 2,an existence condition is studied,that is,the multiscale function is balanced and its corresponding multiwavelet is Armlet.Firstly,a conclusion is proved that when PTST is performed on the orthogonal multiwavelet constructed by a particular algorithm,it not only balances the multiscale function,but also Armlet is the transformed multiwavelet function.Secondly,the case of orthogonal symmetry is also discussed.Finally,the corresponding construction algorithm and examples are given.In chapter 3,the properties and construction algorithm of two-dimensional four-way matrix-valued wavelet are studied,and the construction algorithm of short-supported multi-scale two-dimensional four-way orthogonal matrix-valued wavelet is provided,and the orthogonal formula of two-dimensional four-way matrix-valued wavelet packet is obtained.By analyzing the properties of the wavelet packet,a new Riesz basis in the two-dimensional four-way matrix-valued function is obtained. |
