| 一种新的三维MDCT的快速算法 |
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| 引用本文： | 周茜,伍家松,董志芳,舒华忠.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). |
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| 作者姓名： | 周茜 伍家松 董志芳 舒华忠 |
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| 作者单位： | 东南大学影像科学与技术实验室,南京,210096 |
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| 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) |
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| 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N1×N2×N3的三维MDCT转化为(N1/2)×(N2/2)×(N3/2)的三维离散余弦变换Ⅳ型(DCT-Ⅳ)(N1=2m1,N2=2m2,N3=2m3),然后将后者转化为8个长度为(N1/4)×(N2/4)×(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.
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| 关 键 词： | 三维MDCT 三维DCT 快速算法 |
A fast algorithm for computation of 3-D MDCT |
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| Zhou Qian,Wu Jiasong,Dong Zhifang,Shu Huazhong.A fast algorithm for computation of 3-D MDCT[J].Journal of Southeast University(Natural Science Edition),2010,40(1). |
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| Authors: | Zhou Qian Wu Jiasong Dong Zhifang Shu Huazhong |
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| Institution: | Laboratory of Image Science and Technology;Southeast University;Nanjing 210096;China |
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| 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 N_1×N_2×N_3 is converted into 3-D type-Ⅳ discrete cosine transform (DCT-Ⅳ) with block size (N_1/2 × (N_2/2)×(N_3/2) (N_1 = 2~m_1> ,N_2 =2~m_2> ,N_3=2~m_3>). Secondly, the DCT-Ⅳ is transformed to eight 3-D type-Ⅱ discrete cosine transform (DCT-Ⅱ) with block size (N_1/4)×(N_2/4)×(N_3/4). Finally, a fast algorithm is pro-posed for computing the 3-D DCT- Ⅱ. The analysis of the proposed algorithm in terms of computa-tional 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 sig-nal processing tasks. |
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| Keywords: | 3-D modified discrete cosine transform 3-D discrete cosine transform fast algorithm |
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