摘要
该文简要地分析了在基于小波变换的图像和视频编码中小波基的选择对编码效率和编码质量的影响 .从适于提取图像和视频信号高频成分的角度 ,提出了根据时 -频分辨特性对 B样条双正交小波进行选择的标准 .给出了 B样条小波的构造过程和计算时 -频窗面积的方法 ,并对 2 N 2 0的 N阶 B样条函数 ,得出了使其分析小波函数具有最优时 -频分辨特性的条件 .该条件表明 :B样条函数的阶数较低时 ,其分析小波函数的时 -频分辨特性较好 ,并且 N取偶数时的 B样条双正交小波的时 -频分辨特性要相对优于 N取奇数时的 B样条双正交小波的时 -频分辨特性 .据此条件 ,可以求出相应的对偶尺度函数和小波函数 .最后 ,通过选用几个典型的双正交小波进行编码模拟实验 。
Biorthogonal wavelets have recently received considerable attention in the context of image and video processing due to their linear phases and compact supports. The wavelet representation provides a multiresolution expression of a signal with localization in both time and frequency. However, how to choose proper biorthogonal wavelet bases in the wavelet transform is an important and disputable issue. A majority of papers are focused on regularity condition,coding gain,peak signal to noise ratio (PSNR) and entropy , etc, while seldom take time frequency resolution property into account that is regarded as a key character in many applications such as studying texture and edge features of images and videos. This paper concisely analyzes the influence of the choice of wavelet bases on coding efficiency and quality when image and video coding are based on the wavelet transform. From the point of view suitable for extracting high frequency components of image and video signals, the paper presents the standard of the choice of B spline biorthogonal wavelets according to time frequency resolution property, and gives the construction process of B spline biorthogonal wavelets. A method is proposed in the paper, which can be used for calculating the area of time frequency window. Moreover, as for every B spline function with N order ( 2N20 ), the condition of its decomposition wavelet with optimum time frequency resolution property is given, which suggests that the lower the order of B spline function is, the better the time frequency resolution property of its decomposition wavelet is, and that the time frequency resolution property of B spline biorthogonal wavelets with even orders is comparatively superior to that of B spline biorthogonal wavelets with odd orders. On this condition, corresponding dual scaling function and wavelet can be obtained. Finally, encoding simulation experiments are made to estimate 2D motion vector fields of some test image sequences based on the variable block size multiresolution motion estimation (MRME) approach with several typical biorthogonal wavelets. It is showed that the B spline function with lower order has a superior performance in terms of the PSNR of prediction error frames as well as the entropy of motion vectors. Thus the conclusion is verified.
出处
《计算机学报》
EI
CSCD
北大核心
2002年第4期430-437,共8页
Chinese Journal of Computers
