二维各向同性不可分小波变换特性分析

从滤波器设计、采样方面与标准二维可分小波变换的比较、分析二维各向同性不可分小波变换在图像处理中表现出来的特性,并针对不可分小波提出了新的父子关系定义和改进型零树结构.二维不可分小波变换相对标准可分小波变换而言,尺度函数和小波函数不可分且各向同性,具有更细的渐进尺度,更好的紧支撑特性,各个子带有清晰的频率特征及重建特性.本文通过实验统计分析了二维不可分各向同性小波特性,利用改进型零树结构大大提升了其在图像压缩中的性能;对不可分小波变换在图像处理中的应用具有指导性的意义.

Analysis on 2-D Nonseparable and Isotropic Wavelet Transform

Compared with 2-D separable wavelet the properties of 2-D nonseparable wavelet are analyzed from the aspects of filter design, sampling and others. For special nonseparable wavelet, a new father-son relationship and modified zero-tree structure are proposed. For 2-D nonseparable wavelet transform, its scale and wavelet functions are nonseparable and isotropie, and it has more progressive scales and more tight energy support. Each subhand has more specific frequency feature and eould gain better reeonstruction, This paper analyzes the properties by experimental data, increasing greatly the image compression performance by the modified zerotree and also providing guide for 2-D nonseparable wavelet in image processing.