图像小波系数的分布规律及其对图像质量的影响

Distribution of wavelet coefficients and the effect to the image quality

文中研究了小波系数的统计特性 ,小波系数的均值、方差和能量 ,不同分辨率级相同方向上小波系数的关系 ,以及同一分辨率级不同方向的小波系数对图像主观质量的影响。从而为基于小波变换的图像数据压缩中的量化方法提供了依据 ,得到以下结论 :1 能量主要集中在低频系数 ,它对图像质量的影响最大 ,应对其进行精细量化 ;2 高频系数代表图像的细节信息 ,分辨率级越高的高频系数 ,对图像质量的影响越小 ,量化可以越粗 ;3 对同一方向不同分辨率级的高频系数 ,由于其相似性 ,可采用零树量化方法 ;4 在同一分辨率级 ,对角方向的系数对图像质量的影响最小 ,对角方向的系数量化最粗。

In this paper, the wavelet coefficients statistical characteristics, average, variance and energy are studied, the wavelet coefficients relation in different resolution of the same direction and the relation of the coefficients in the same resolution with different directions are analyzed, and the effect of wavelet coefficients to the visual quality of the reconstructed image is disscussed. The works in the foregoing content provide the foundation for the quantization method of compacting image code which is based on the wavelet transform, and the conclusions are as following: 1. The energy is mainly focused on the low frequency coefficient, and the maximal effect to image quality is from these coefficients, the fine quantization should be applied for; 2. The high frequency is related with the image detail, the higher is the level of the resolution power, the lesser is the effect of the high frequency coefficient to the image quality, and quantization can be coarser; 3. As far as the high frequency coefficient, which is in the same direction but not the same level of resolution, as the comparability, zero tree quantization can be used; 4. The effect to the image quality of the dragonal coefficients, which is in the same resolution is the least, and the quantization of these coefficients is the most coarsest.