Wei D, Tian J, Wells R R, Burrus C S
Dept. of Electr. and Comput. Eng., Rice Univ., Houston, TX 77251-1892, USA.
IEEE Trans Image Process. 1998;7(7):1000-13. doi: 10.1109/83.701157.
We construct general biorthogonal Coifman wavelet systems, a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair. A time-domain design method is employed and closed-form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived. The resulting filter coefficients are all dyadic fractions, which is an attractive feature in the realization of multiplication-free discrete wavelet transform. Even-ordered systems in this family are symmetric, which correspond to linear-phase dual filters. In particular, three filterbanks (FBs) in this family are systematically verified to have competitive compression potential to the 9-7 tap biorthogonal wavelet FB by Cohen et al., which is currently the most widely used one in the field of wavelet transform coding. In addition, the proposed FB's have much smaller computational complexity in terms of floating-point operations required in transformation, and therefore indicate a better tradeoff between compression performance and computational complexity.
我们构造了一般双正交Coifman小波系统，这是一类新的具有紧支集的双正交小波系统，其尺度函数和小波对的消失矩均匀分布。采用时域设计方法，推导了相应对偶滤波器的脉冲响应和频率响应的闭式表达式。所得滤波器系数均为二进分数，这在无乘法离散小波变换的实现中是一个吸引人的特性。该族中的偶阶系统是对称的，对应于线性相位对偶滤波器。特别是，该族中的三个滤波器组（FBs）被系统地验证与Cohen等人提出的9-7抽头双正交小波FB相比具有竞争的压缩潜力，9-7抽头双正交小波FB是目前小波变换编码领域中使用最广泛的。此外，所提出的FBs在变换所需的浮点运算方面具有小得多的计算复杂度，因此在压缩性能和计算复杂度之间显示出更好的权衡。
