参数化的Deslauriers-Dubuc插值小波——构造及图像编码性能分析

研究了采用提升构造具有任意偶数阶消失矩, 满足对称性, 且仅用一个自由参数表达的 Deslauriers-Dubuc (D-D)双正交插值小波. 首先,采用多相矩阵理论推导出了此类小波存在的条件; 然后,给出了对应小波滤波器和插值小波变换的构造算法. 采用算法具体构造了分别具有消失矩对(4, 2)、(4, 4)、(6, 2)以及(6, 4) 等4类一参数表达的D-D插值小波; 最后, 以自由参数为自变量, 根据编码增益准则, 优化设计了4种用于图像编码的插值小波, 其滤波器系数全为二进制分数, 可实现非乘法运算的离散小波变换(Discrete wavelet transform, DWT). 系统分析表明, 两种小波的压缩性能超过CDF-9/7小波, 对于纹理图像, PSNR增益达到0.44.dB, 并且计算复杂度可降低17%以上. 实验同时表明, 新小波的重构图像具有更好的主观可视质量.

Parametric Deslauriers-Dubuc Interpolating Wavelets:Construction and Performance Analysis for Image Coding

This paper mainly focuses on how to construct new parametric Deslauriers-Dubuc (D-D) biorthogonal interpolating wavelets which have arbitrary vanishing moments, symmetry, and depend on one free parameter via lifting scheme. We first derive their existence conditions necessary for the wavelets with the polyphase matrix theory. Then, we demonstrate the detailed algorithm for constructing their associated wavelet filter bank and interpolating wavelet transforms. With the algorithm, four classes of parametric D-D wavelets with vanishing moment pairs of (4, 2), (4, 4), (6, 2) and (6, 4), respectively are constructed. Finally, according to the coding gain criterion, we design four new interpolating wavelets for image coding by adjusting the free parameter; they all have dyadic-fraction filter coefficients and can realize a multiplication-free DWT. Extensive simulations show that the two interpolating wavelets exhibit performances superior to the CDF-9/7 wavelet, especially with a gain of up to 0.44.dB in PSNR over the latter for rich-textured image and a lower computational cost by 17%. In addition, significant improvement in subjectively visual quality is also observed.