The Biorthogonal Compactly Supported Wavelets Construction And Application Research

With the rapidly development of wavelet analysis,it is used widely in theory and practical applications since the Haar wavelet bases was introduced in 1909.The wavelet’s advantages are the time-frequency domain localizations, multiresolution properties and Mallat fast algorhthm.The wavelet transform is an effective method in signal and image processing since the wavelets analysis were improved by Daubechies, Mallat, et al.The orthogonal compactly supported wavelets have perfect mathematical expression and simple calculation.The biorthogonal compactly supported wavelets have more excellent performance on the high vanishing moment,regularity and linear phase than that of orthogonal wavelets.According the Bezout theorem,the constraint conditions which the biorthogonal compactly supported wavelets satisfy are composed of linear and quadratic equations.The solutions quantity is decided jointly by the scaling function (?)(t) vanishing moment N and dual scaling function (?)(t) vanishing moment N.The biorthogonal wavelets available now are only some particular examples of total solutions.The constraint conditions are constructed when the vanishing moment’s sum L=1/2(N+N], L= 2,3,···,7 are given.The total biorthogonal wavelets are constructed in which the global convergent hmotopy method is used for different N and N.The N and N must have the same parity which makes L is an integer. The different property of (?)(t) and (?)(t) are constructed by N, N and selecting different solutions of constrain equations.The properties including filters coefficients,supports width and symmetrical centers of (?)(t),(?)(t),Ψ(t) and Ψ(t) are disscuessed in detailed.The time domain waveform,amplitude and phase spectrum are plotted.An image compressed method based on HVS and potential function clustering is presented. The image is divided into smooth and non-smooth sub-image using the multi-threshold-segmentation method.The biorthogonal compactly supported wavelets which is constructed in the thesis are used as the core of wavelets transform.The method overcomes the defects which the DCT and quantization table are both 8×8 pixels and could not varied with the different image. The algorithms improve the image compression rate of 10% at least. The experiment verifys the validity of algorithm.