高性能、有理系数9/7双正交小波滤波器组的设计

提出了一种构造9／7双正交小波的新方法．在给定用一个参数表达的9／7合成滤波器的前提下，把双正交小波的精确重构条件表示为一个丢番图方程并求解，得到其分解滤波器，从而得到了9／7双正交小波滤波器组的参数表达式．通过设定该表达式参数为任意不同的实数，可以随意构造具有不同特征的9／7线性相位滤波器．以示例的形式构造了2种高性能的滤波器，一种具有最佳编码增益，另一种系数为二进制分数．理论分析和实验表明：前者具有与CDF9／7滤波器相同的压缩性能和较低的计算复杂度；后者仅采用移位一加就可实现离散小波变换，非常有利于超大规模集成电路的高效实现．

Design of 9/7 Biorthogonal Wavelet Filter Banks with Rational Coefficients and High Performance

A new technique to construct the 9/7 biorthogonal wavelets was presented. Given the 9/7 synthesis filter represented by a free parameter, the perfect reconstruction condition of the filter bank was formulated as a Diophantine equation, and was solved. Thus, the exact free parameter expressions for the 9/7 biorthogonal wavelet filter banks were derived. By assigning arbitrarily different real numbers to the free parameter, any linear phase 9/7 filter (a pair) with different features could be constructed. As a case study, two kinds of high performance filter banks were constructed, and one had optimal coding gain and rational coefficients whereas the other had coefficients that were approximated by dyadic fractions. Both theoretical analysis and extensive simulations show that the former filter bank has the same compression performance as the popular 9/7 filter bank by Cohen, Daubechies, and Feauveau for image transform coding, and yet requires lower computational complexity; the latter filter bank has the advantage that its discrete wavelet transform (DWT) can be realized by the shift-add operation, which benefits highly efficient implementation of DWT via very large scale integration.