The Construction Of Binary Multiwavelets And Their Frameworks

For bivariate multi-wavelets and wavelet frames have obvious validity in image processing,so it is important to study bivariate multi-wavelets and wavelet frames.At present,the research of wavelet generated by single scale function and its wavelet frames has many important conclusions,but the research of bivariate wavelets and wavelet frames generated by multiple scale functions is rare.Based on the two-direction wavelet and the minimum-energy wavelet frames,this paper introduces the two-direction wavelet and the minimum-energy wavelet frames into the high-dimensional signal.Firstly,the basic concepts and properties of twodirection multi-wavelet and minimum-energy multi-wavelet are analyzed and summarized.Secondly,based on the concept of bivariate four-direction multi-scaling functions and bivariate four-direction multi-wavelets,the bivariate four-direction orthogonal multi-wavelets with dilation factor two are generalized to bivariate biorthogonal multi-wavelets with dilation factor ?.The construction algorithm of bivariate biorthogonal multi-scaling functions and multi-wavelets with dilation factor ? are given.The Mallat algorithm of bivariate four-direction multi-wavelets with dilation factor ? is studied.Finally,based on the minimum-energy multi-wavelet frames,the concept of bivariate minimum-energy multi-wavelet frames with dilation factor ? and the sufficient and necessary conditions for satisfying the characteristics of bivariate minimum energy multi-wavelet frames are given.Via using the polyphase decomposition that corresponds to the symbol functions for scaling function and wavelet function,the decomposition and reconstruction algorithms of bivariate minimumenergy multi-wavelet frames with dilation factor ? are presented.