一维F转换压缩算法转换系数大纲的构造中国图象图形学报.DOC

中图法分类号：TN919.81 文献标识码：A 文章编号：1006-8961( ) 论文引用格式： L∞准则的最大误差图像压缩算法 李晓云1,2 ， 庞超逸2，3 ， 黎彤亮2，黄世中2 1.石家庄开发区冀科双实科技有限公司, 石家庄 050081； 2.河北省科学院应用数学研究所，石家庄 050081； 3.澳大利亚联邦科学院电子健康研究中心, 布里斯班compression based on L∞ norm Li Xiaoyun1,, Pang Chaoyi2,3, Li Tongliang3 , Huang Shizhong3 1. S J Z J K S S Technology Co., Ltd, Shi jiazhuang 050081, China; 2. The Applied Mathematics Institute, Heibei Academy of Science, Shi jiazhuang 050081,China；3. The Australian e-Health Research Centre, CSIRO, Melbourne 3000 , Australian Abstract: Objective: Traditional image compression algorithms are mostly based on L2 norm. However, those methods are not able to precisely control the error of each point. In this paper a maximum error image shift compression algorithm based on L∞ norm is proposed. The algorithm can guarantee that the error at each point of the reconstructed image is limited in a given range. Method: First，the algorithm takes the advantage of the image pixel similarity to decompose the image into many non-overlapping sub-blocks. Then each sub-block should be completely shifted, and the retained shift coefficients must be stored. Finally, the original image can be reconstructed by the retained shift coefficients. Result: The experimental results show that, the suitable block size of the images of different resolutions is not the same, which increases by the increase of image resolution. Conclusion: Compared with the existing algorithm based on L∞ norm maximum error shift compression, the compression ratio, reconstructed image quality and compression speed can be improved by the proposed algorithm. Key words: shift compression; L∞ norm; maximum error; image compression 0 引 言 传统的图像压缩算法大多是基于均方误差准则(L2范数)下的压缩算法[1-4]。该准则简单优美，普遍应用于信号和图像处理等方面。然而该准则是基于数据的整体特性来度量的，因此用户不能控制每个数据点的误差，可能导致个别点出现较大的偏差，而基于L∞准则的压缩算法能够使得每一个数据点的重构误差小于给定的误差限。因此引起了许多相关学者的关注[5-7]。 一维L∞最大误差压缩算法是二维L∞最大误差压缩算法应用的基础，目前研究较多的是一维L∞最大误差压缩算法。基于L∞准则的二维最大误差压缩算法非常少。Garofalakis通过引入小波大纲第一次提出了基于L∞准则的小波压缩技术[1]，由于其采用的是