用多项式变换计算多维离散W变换

1．引言多维离散W变换作为多维离散Hartley变换的推广［1－3］，是处理多维问题的一种工具．在计算机视觉、高清晰度电视（HDTV）以及可视电话等领域，经常要对运动图象进行分析和处理，通常称为多帧检测（Multi－WameDetection，简称MFD）［4－5］，这时三维离散w变换是一种可行的方法．由于不需要进行复数运算，比三维离散傅立叶交换（DFT）有优越性．而对运动的三维图象进行处理时，可采用四维离散w变换．对维数更高的多维信号进行处理时，可采用多维离散w变换．对三维以上的w变换，需要的运算量非常大，设计好的快速算法极为重要…

COMPUTING MULTI-DIMENSIONAL DISCRETE W TRANSFORMS BY POLYNOMIAL TRANSFORMS

In this paper, the Multi-dimensional Polynomial Transform is used to convert the Multi-dimensional W Transform (MDDWT) into a series of one-dimensional W transform (DWT). Thus, a new polynomial transform algorithms for MDDWT is obtained. The algorithm needs no complex number operations and is simple in structure. The number of multiplications for computing a r-d DWT is only times that of the common used row-column method. The number of additions is also reduced considerablely. Running time of the algorithm on micro-computers is given and is compared with the common used row-column method.