The Design And Its Applications Research Of Multiband Coifman Wavelets

Wavelet theory has become one of the most important tool used in information science and applied mathematics, it is virtual that the wavelet is used in fundamental theory s and applied sciences. Science image is the most used object, the combination of new wavelet and its fast algorithm and the partialdifferential equation(s) are suitable for digital image processing and has been extensively used, this is the mainly contents studied in the paper.In this paper we study construction of the multi-band Coifman wavelet from the viewpoint of filter bank, and furthermore, we consider removing the noised signal by using combination of the wavelet and pirtial differential equation(s). The contrubitation of this paper is as follwos:1,Genearilaze the concept of the known Coifman wavelet, and under the frmae of 2-band perfect reconstruction, we give a simple construction method for 2-band Coifman wavelet.2,By discussing the polyphase express of multi-band filter and its properties, and using combination of the fundmental theory for multi-band Coifman type of biorthogonal perfect reconstruction filter, we propose a kind of linear equation method for solving multi-band Coifman type of scaling filter.3,By introducing vanishing moment property, using scaling function we achieve the coefficients of low-pass filter,and the orther high-pass filter is also obtained by a new modulation, and the cosine-modulation technique is a special example appeared in this paper.4,Together with the wavelet and partialdifferential equation(s) is proposed to be used for removing noise occurred in image. In the first, we propose three coefficients Trivariate Shrinkage method, using this technique and geometry curvature-driven diffusion, a new high quality image noisy removal is obtained.