[1]周茜,伍家松,董志芳,等.一种新的三维MDCT的快速算法[J].东南大学学报(自然科学版),2010,40(1):75-79.[doi:10.3969/j.issn.1001-0505.2010.01.014]
 Zhou Qian,Wu Jiasong,Dong Zhifang,et al.A fast algorithm for computation of 3-D MDCT[J].Journal of Southeast University (Natural Science Edition),2010,40(1):75-79.[doi:10.3969/j.issn.1001-0505.2010.01.014]
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一种新的三维MDCT的快速算法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
40
期数:
2010年第1期
页码:
75-79
栏目:
计算机科学与工程
出版日期:
2010-01-20

文章信息/Info

Title:
A fast algorithm for computation of 3-D MDCT
作者:
周茜 伍家松 董志芳 舒华忠
东南大学影像科学与技术实验室, 南京 210096
Author(s):
Zhou Qian Wu Jiasong Dong Zhifang Shu Huazhong
Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China
关键词:
三维MDCT 三维DCT 快速算法
Keywords:
3-D modified discrete cosine transform 3-D discrete cosine transform fast algorithm
分类号:
TP301.5
DOI:
10.3969/j.issn.1001-0505.2010.01.014
摘要:
提出了计算三维改进的离散余弦变换(MDCT)的一种快速方法,可以有效减小数据量,提高计算机存储和运算的效率.首先将序列长度为N1ҿN2ࢧN33的三维MDCT转化为(N1/12)×(N2/22)×(N3/32)的三维离散余弦变换Ⅳ型(DCT-Ⅳ)(N1=12m1,N2=122m2,N3=232m33),然后将后者转化为8个长度为(N1/14)×(N2/24)×(N3/4)的三维离散余弦变换Ⅱ型(DCT-Ⅱ),最后再通过变量代换和加法运算实现整个快速计算过程.同时,通过编写程序验证算法的正确性,并分析该算法的计算复杂度.结果表明:较之传统的行列方法,所提出的算法能够有效使计算复杂度降低75%左右,实现了计算机在三维信号处理领域的运行速率的提高.
Abstract:
A novel fast algorithm for the computation of 3-D modified discrete cosine transform(MDCT)is proposed, which can reduce the amount of data effectively and improve the storage and computing efficiency. Firstly,the 3-D MDCT with block size N1ҿN2ࢧN33 is converted into 3-D type-Ⅳ discrete cosine transform(DCT-Ⅳ)with block size(N1/12)×(N2/22)×(N3/32)(N1=12m1,N2=122m2,N3=232m33). Secondly, the DCT-Ⅳ is transformed to eight 3-D type-Ⅱ discrete cosine transform(DCT-Ⅱ)with block size(N1/14)×(N2/24)×(N3/34). Finally, a fast algorithm is proposed for computing the 3-D DCT-Ⅱ. The analysis of the proposed algorithm in terms of computational complexity is provided. The proposed algorithm achieves about 70% reduction of arithmetic operations compared to the traditional row-column method, and could find its application in 3-D signal processing tasks.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 周茜(1986—),女,硕士生; 舒华忠(联系人),男,博士,教授,博士生导师,shu.list@seu.edu.cn.
基金项目: 国家自然科学基金资助项目(60873048)、江苏省自然科学基金资助项目(BK2008279,BK2009012).
引文格式: 周茜,伍家松,董志芳,等.一种新的三维MDCT的快速算法[J].东南大学学报:自然科学版,2010,40(1):75-79. [doi:10.3969/j.issn.1001-0505.2010.01.014]
更新日期/Last Update: 2010-01-20