Feig DCT算法的矩阵分析与改进

The Matrix Decomposition Representation and Modification of Feig's DCT

摘要: 离散余弦变换(DCT)是图像处理领域广泛使用的一种变换方法,其中,Feig的2D DCT算法被认为是需要加法和乘法操作次数最少的.为了加深对Feig算法的理解和进一步提出更好的快速算法,首先使用简单的矩阵分解理沦来得到Feig的算法和另外3种不同形式的矩阵分解;然后,对Feig的Scaled-DCT算法做进一步研究,消去了其中隐含的49个求相反数的多余操作,并使其结构更加规整,以适合于SIMD和VLIW结构.

Abstract: Discrete cosine transforms(DCT's)are the mainstay of image signal processing.So far as is known,Feig's 2D DCT requires the least number of operations.In order to help understanding Feig's algo- rithm and further improve the algorithm,this paper first utilizes simple matrix decomposition theory to obtain Feig's algorithm.In addition,Feig's algorithm is extended to other three forms.Then,we further elimi- nates the inherent 49 negative operations of Feig's algorithm and regularizes its data flow diagram which is suitable for SIMD and VLIW.