对提升后的Donoho小波进行了进一步研究,通过正则性的计算和小波采样逼近理论说明N=N~=4(记为SWE13/7)时有较好的逼近性能,并在采样逼近上优于D9/7小波。SWE13/7的提升系数是简单分数,从而可以得到在计算过程中仅使用到整数位移和加法的提升格式,使计算复杂性大幅度低于D9/7小波,而且结果等价于中间过程使用浮点数运算时的结果。基于行的提升格式可以大幅度减少内存使用量,并在并行计算时提高计算速度,本文实现了SWE13/7的基于行的提升格式,它的计算量也明显小于D9/7。数值实验结果说明使用零树编码时,SWE13/7的图像压缩效果整体上优于D9/7效果,并且计算量小很多。

This paper does further research for the lifted Donoho wavelets.Through the computing of regularity and the wavelets sampling approximation theory,we explain it has better approximation capability when N=N~=4(denoted as SWE13/7),and it precedes D9/7 wavelets in sampling approximation.The lifting coefficients of SWE13/7 are all simple fractions,so wavelets transform only with integer shift and adder operations can be obtained in computing process,the computing complexity is efficiently lower than D9/7,and the result is equivalent to those using floating number in computing process.The line-based lifting scheme can efficiently decrease the memory usage,and increase the speed at parallel computing case.This paper has realized the line-based lifting scheme of SWE13/7,it has lower complexity than D9/7 in evidence.Numerical experiments indicate that the image compression performance of SWE13/7 precedes that of D9/7 when using EZW coding,and its computing complexity is much less.