最优多进Haar小波及在图像压缩中的应用  

OPTIMAL MULTI-BANK HAAR WAVELETS AND THEIR APPLICATION IN IMAGE COMPRESSION

作　　者：王国秋[1] 全宏跃[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《计算数学》2009年第1期99-110,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目(10571049).

摘　　要：我们提出了最优多进Haar小波的概念,证明了其存在性和唯一性,给出了最优多进Haar小波构造的通用方法,并证明了最优多进Haar小波具有线性相位.在消失矩意义下,我们所得到的最优多进Haar小波优于离散余弦变换.同时,我们用图像缩编码的方法验证了最优多进Haar小波的性能优于离散余弦变换的.新的变换可以化为精确的小整数运算,能非常廉价地用集成电路实现.该变换的实用意义在于给图像和视频压缩提供了一个更好的选择.We have put forward a concept of optimal multi-bank Haar wavelets, shown the existence and the uniqueness, and given a general method of constructing the optimal multi-bank Haar wavelets, and also shown that the optimal multi-bank Haar wavelets have the linear phase. Theoretically, the wavelets constructed in this paper are superior to the discrete cosine transform （DCT） in the meaning of vanishing moments. Also, we have shown experimentally that the optimal multi-bank Haar wavelets perform better than DCT in image compression. New transforms can be implemented with IC economically due to the precise computation of small integers. The applicative significance of new transforms is to provide a better choice for image or video compression.

关 键 词：多进小波 图像压缩 最优Haar小波 JPEG 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]