基于多项式运算的无累积误差Loeffler DCT算法  

Cumulative error-free Loeffler DCT algorithm based on polynomial calculations

作　　者：沈永珞[1] 章媛[2] 杨迪威[3] 李璇[1] 

机构地区：[1]广东财经大学信息学院,广东广州510320 [2]国家知识产权局专利局专利审查协作广东中心,广东广州510530 [3]中国地质大学(武汉)数学与物理学院,湖北武汉430074

出　　处：《计算机工程与设计》2014年第11期3855-3858,3912,共5页Computer Engineering and Design

基　　金：国家自然科学基金青年科学基金项目(61300108)

摘　　要：为避免离散余弦变换(DCT)中的乘法操作以及运算过程中的累积误差,提出一种基于多项式运算的Loeffler DCT算法。将传统Loeffler DCT算法的流程分成3个模块:常规数值运算模块、多项式运算模块和结果再生模块;通过多项式运算,DCT算法中涉及到的无理数乘法操作被分解成简单的整数加减及移位运算。分析和实验结果表明,该算法能完全避免乘法操作,且由于无计算累积误差,在图像处理过程中能保证较高的图像质量。To avoid multiplications and cumulative errors during the discrete cosine transform, a multiplication-free Loeffler DCT algorithm based on polynomial calculations was presented. The proposed algorithm consisted of three modules including the nor- mal integer calculation module, the polynomial calculation module and the final result reconstruction module. At the mean while, the multiplications with irrational constant values in the DCT calculations were replaced by the integer adding and shift operations through polynomial transforms. The analysis and experiment results show that multiplications can be avoided and the high image quality can be achieved due to none cumulative errors using this method.

关 键 词：离散余弦变换 多项式运算 无乘法DCT 累积误差 算法设计 

分 类 号：TN911.73[电子电信—通信与信息系统]