多维DCT/IDCT立体类蝶形算法及其单元式通道结构

doi:10.13229/j.cnki.jdxbgxb201606045

摘要/Abstract

摘要： 为了匹配离散余弦变换(DCT)算法不同大小分块,实现不同维度DCT结构的兼容性,提出了一种多维DCT立体类蝶形算法,并对其单元式通道结构进行研究。首先,根据DCT理论,以“张量积”运算为基础,介绍了DCT及其反变换IDCT立体类蝶形算法理论原理,给出了多维算法推导。然后,以DCT/IDCT立体类蝶形算法数学运算为理论基础,从一维引申至多维立体类蝶形图形式,并根据多维与一维的关系,以一维单元式通道结构为基础,提出多维单元式通道结构。实验结果表明:本文算法仅需要传统算法中50%的加法器和约30%的乘法器;算法耗时与分块大小和维度有关,在从三维到五维的实验耗时检测中,本文算法耗时不超过普通DCT算法耗时的10%,具有速度快、复杂度低、多维兼容性的特点。

关键词: 信息处理技术, DCT/IDCT, 多维立体, 蝶形算法, 通道式结构

Abstract: In order to match different size block of Discrete Cosine Transform (DCT) algorithm, the architecture compatibility of different dimensional DCTs is implemented. A multidimensional DCT similar butterfly algorithm is proposed and its unit channel architectures are studied. First, based on the theory of DCT and tensor product operation, the theoretical principles of the DCT similar butterfly algorithm and its inverse transform IDCT are introduced, and the derivation of the multidimensional algorithm is given. Second, taking the arithmetical operation of DCT/IDCT stereo similar butterfly algorithm as the theoretical foundation, the one-dimensional stereo similar butterfly diagram is extended to multidimensional one. Finally, according to the relationship of one-dimension and multi-dimension, based on the one-dimensional channel unit architectures, the multidimensional unit channel architectures are put forward. Experimental results indicate that the proposeds algorithm only needs 50% adders and 30% multipliers of the traditional algorithm. The consuming time of this algorithm is related to the block size and dimension, for three-dimension and five-dimension, the consuming time of this algorithm is less than 10% of that of the common DCT algorithm. This algorithm is characterized by fast, low complexity and multidimensional compatibility.

Key words: information processing, DCT/IDCT, multidimensional stereo, butterfly algorithm, pipeline architectures

中图分类号:

TN919

刘媛媛, 陈贺新, 赵岩, 杨楚皙. 多维DCT/IDCT立体类蝶形算法及其单元式通道结构[J]. 吉林大学学报(工学版), 2016, 46(6): 2094-2102.

LIU Yuan-yuan, CHEN He-xin, ZHAO Yan, YANG Chu-xi. Multidimensional DCT/IDCT similar butterfly algorithm and it unit channel architectures[J]. 吉林大学学报(工学版), 2016, 46(6): 2094-2102.

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