Construction Method Of Binary Even Bands Dual Wavelet Tight Frames

Wavelet analysis is the disciplines of profound mathematical theory and a widerange of applications, which is developed in recent thirty years, and the waveletframes are one of the most important research topics in wavelet analysis. Comparedwith wavelet frames, wavelet tight frames have many good properties. Wavelet tightframes are similar to a sequence of orthogonal wavelet bases, therefore it has lots ofthe good properties of orthogonal wavelet bases.So far, construction method of binary2-band,3-band,4-band and6-bandwavelet tight frames has been given by people. Because the number of bands has agreat degree of influence on signal processing effect. Therefore increasing thenumber of bands is a kind of inevitable means to enhance the high-frequency signalprocessing effect. With the number of bands increasing, the effect is better in signalprocessing. So, the study of multiple bands dual wavelet tight frames is verymeaningful. It is due to the flexibility of the frame representation that makingwavelet tight frames have been widely used in signal processing, image compression,numerical calculation etc.On the basis of these, firstly, with the help of multi-resolution analysis methodand mainly using frame multi-resolution analysis, the construction method of binaryeven bands wavelet tight frames is given, which can construct the correspondingwavelet tight frames if any even orders unitary matrix is given. Although a largeamount of calculation, and certification process is very complex, this method makesthe construction method of wavelet tight frames more general.Secondly, in the process of restoring signal using wavelet tight frames, forconvenience of numerical calculation, the decomposition and reconstructionformulas of binary even bands wavelet tight frames are discussed, and numericalexample is given.Finally, the binary even bands dual wavelet tight frames are constructed by theproperties of scaling function, and strict proof is given.