提升式5/3二维离散小波变换的小波系数位宽整定  

Estimation of Wavelet Coefficients Range for Lifting-based 5/3 2-D Discrete Wavelet Transform

作　　者：毛曼卿[1] 王春林[1] 陈卓[1] 刘克刚[1] 

机构地区：[1]武汉大学电子信息学院

出　　处：《电子技术（上海）》2012年第11期17-20,共4页Electronic Technology

摘　　要：相对于JPEG中二维离散余弦变换(DCT)来说,在JPEG2000标准中,二维离散小波变换(DWT)是图像处理的核心变换。然而在小波变换过程中,有一个不可避免的问题,就是小波系数的动态范围的确定,它直接决定计算精度以及存储空间的利用率。文章针对5/3提升小波算法的硬件架构,在理论分析中进行了三次小波系数动态范围的整定并给出详细的数学推导。最后得到的位宽数是对以往宽泛结论的较为精确地整定。可以在保证运算精度的前提下,避免增加无谓的硬件资源和存储器。最后使用Matlab对标准图像进行一到五级的小波分解,验证了该结论的有效性。Relative to 2 D discrete cosine transform （DCT） in JPEG, in JPEG2000 standard, 2D discrete wavelet transform （DWT） is the core transformation of image processing. However, in the process of wavelet transform, there is an inevitable issue, the determination of dynamic range of the wavelet coefficients, which directly determines the computational accuracy and utilization of storage space. Aiming at the hardware architecture of the 5/3 lifting wavelet algorithm, this paper carries out three times of tuning of the wavelet coefficients dynamic range and gives a detailed mathematical derivation in the theoretical analysis. The final number of the bit width is the accurate tuning to the past broad conclusions. On the basis of ensuring operation accuracy it could avoid adding unnecessary hardware resource and memory. Finally the paper uses Matlab to carry out wavelet decomposition from 1 to 5 classes, thereby verifying the validity of the conclusions.

关 键 词：离散小波变换 提升式算法 小波系数 位宽范围 

分 类 号：TN919.81[电子电信—通信与信息系统]