一种新型双正交小波滤波器的设计

Design of Biorthogonal Wavelet Filters

本文提出了一种从对称正则滤波器中得到一系列对称双正交小波的新技术,其主要思路是找出所给出滤波器的一个对称互补正则滤波器,这样得到的滤波器与理想半谱带滤波器之间存在最小二次方振幅偏差。因此,从给出的正则对称滤波器,或者从已知的对称双正交小波,都可以很容易得到一系列带有更好频率选择特性的对称双正交小波滤波器组。一旦找到互补滤波器,此互补滤波器的另外一个互补滤波器也就可以以同样的方法得到。系列双正交小波滤波器源自于标准An-otonini9/7双正交小波。应用此小波滤波器来压缩著名的Lena、Barbara和Goldhill等图像,改善了峰值信噪比(PSNR)。

A technique for deriving a new symmetric biorthogonal wavelets from a given symmetric regular filter is presented.The main idea is to find a symmetric complementary regular filter of the given filter which has the least square amplitude deviation from the ideal half-band filter. Thus from given regular symmetric filter, or from a known symmetric biorthogonal wavelet, a new symmetric biothogonal wavelet filter banks with better frequency selectivity can easily be designed.Once the complementary filter is found out, another complementary filter of this complementary filter can again be obtained in the same way. Particularly, a new biorthogonal wavelet filters are derived from the standard Anotonini 9/7 biorthogonal wavelets.Applying these wavelet to filters to compression of the well known images of Lena, Barbara and Goldhill, etc, improved results in PSNR, are achieved.