【作者】 王亚君； 刘晓冬； 戴琼海； 李俊；

【Author】 Yajun Wang, Xiaodong Liu, Qionghai Dai, Jun Li (Graduate school at Shenzhen, Tinghua University, Shenzhen 518055, China)

【机构】 清华大学深圳研究生院；

【摘要】 在目前广泛应用的小波压缩技术中,由于多维可分离小波方向性上的跳棋盘效应局限了其进一步发展,根据复小波理论可以在原理上消去这些失真,但存在取实部困难问题。本文提出一种双树离散小波变换技术并给出了变换公式及变换方法。仿真结果显示,该方法很好地解决了视频图像的跳棋盘效应。更多还原

【Abstract】 The technology of multi-dimension separable wavelet transform had taken a big development in the recent years, but when it applied for the video compression with motion vectors, for the sake of direction checkerboard artifact, is limited to develop further. A method which based on Dual-tree Discrete Wavelet Transform (DDWT) is proposed in the paper, it can eliminate the checkerboard artifact in video coding validly. The DDWT is combined with Hilbert Transform, and it is based on Kingsbury’s complex wavelet theory. Checkerboard artifact is defined as the mixture phenomenon of orientation expression of motion vectors during the wavelet transform, namely one basis factor has to express two different directional motion vectors, which cause artifact in the image, for example it will mix 45 and -45 degree or 15 and -15 degree orientations. The artifact appeared when the wavelet filter function is a real function and its spectrum must be two-sided in the frequency domain. The method of dual-tree DWT proposed in this paper extended the number of basis factors to express the motion vector, and then the different directional motion vector can be expressed by different basis factor/subband. The dual-tree wavelet transform is implemented by using separable transforms and combining subband signals appropriately. So even though it is non-separable (and therefore free of some of the limitations of separable transforms) it inherits the computational efficiency of separable transforms. We used complex wavelet function to process the image data, and then gained the different direction subband coefficients by taking real-part of complex wavelet transform. The process of taking real-part exploits the character of Hilbert Transform. According to the character of Hilbert Transform we know that its Fourier Transform is inverse in frequency domain, and the transform pair’s value is only dissimilar by a complex symbol as “j”. The complex wavelet function’s Fourier Transform that applied Hilbert Transform only hold the positive frequency to form one-side spectrum, and avoid the checkerboard artifact validly by taking real-part of complex wavelet unconsciously. Hilbert pairs of wavelet bases were studied by Selesnick who had given a characterization and provides a Daubechies-like construction for approximate Hilbert pairs of orthonormal (and biorthogonal) wavelets with vanishing moments and compact support. So we applied the Daubechies-like algorithm for the construction of Hilbert pairs of short orthonormal (and biorthogonal) wavelet bases. Then we applied dual-pyramid filter structure which is attained by dual-tree wavelet to transform the image data, and processed the result by addition or subtraction to gain the exact orientation basis factor/subband coefficients. So the checkerboard artifact is avoided by using the exact motion vectors. In the paper we deduced the correlation of the dual-tree wavelet filters groups’ parameter by analyzing the principle concluded above and the character of wavelet function, and then form the dual-tree wavelet filter structure by applying the Daubechies wavelet to the processing image. We attained real-part and imagine-part filter’s parameters modules that are inversed by differing 1.5 units and the sign of parameters vary with “n”. The emulation result showed that our method have the very good smooth effect and solve the checkerboard artifact of video compression coding successfully. We demonstrated the dual-tree discrete wavelet transform has attractive properties for video representation because of the selectable orientation. For future work, the correlation among adjacent spatial and temporal coefficients needs to be explored. And as we know the 3D DDWT has the similar effect of the motion compensation, then there are maybe a tradeoff between them to optimize the video coding efficiently. How to reduce the coefficients and find the tradeoff is a challenging open research problem.更多还原