17/11双正交小波的优化设计及其对图像压缩性能的分析

许多适合于图像编码的小波，如CDF-9/7，Winger-17/11(W-17/11)，Villasenor-6/10和10/18(V-6/10和V-10/18)小波，其滤波器系数是无理数，需要用无限的计算精度实现对应的离散小波变换(DWT)。该文给出了一种参数化构造17/11双正交小波组的简便方法:首先把小波合成滤波器表示为用两个自由参数表达的三角多项式，然后把双正交小波的精确重构条件归结为一个线性方程组，最后求解此方程组得到对应的小波分解滤波器，从而得到了17/11双正交小波滤波器的参数表达式。通过调整表达式中的自由参数，可以随意构造具有所需特征的17/11线性相位小波滤波器。作为构造实例，构造出一种新的有理系数17/11双正交小波滤波器，它具有优化的编码增益。实验表明:其压缩性能与W-17/11和V-10/18小波滤波器相当，优于CDF-9/7和V-6/10小波滤波器。

Optimization Design of 17/11 Biorthogonal Wavelet and Its Performance Analysis for Image Compression

Many wavelet filter banks suitable for image coding, e.g. CDF-9/7, Winger-17/11 (W-17/11), Villasenor-6/10 and 10/18 (V-6/10 and V-10/18), have irrational coefficients, and thus require infinite computational precision to implement the corresponding Discrete Wavelet Transforms (DWT). Here a simple technique for parametrization construction of 17/11 biorthogonal wavelet family is presented: first, the associated synthesis filter is formulated as one trigonometric polynomial represented by two free parameters; then the perfect reconstruction condition of the filter bank is reduced to one system of linear equations; finally the analysis filter is obtained by solving this system of linear equations. Thus, the exact free parameter expressions for the 17/11 biorthogonal wavelet filter banks are derived. By adjusting the free parameters, one can easily construct any linear phase 17/11 filters (a pair) with desired features. As a case study, a previously unpublished 17/11 biorthogonal wavelet filter bank with rational coefficients is constructed, which has optimum coding gain. Extensive simulations show that the new filter bank has the compression performance comparable to that of W-17/11 and V-10/18 for image transform coding, while surpasses the CDF-9/7 and V-6/10 far away.