图像小波变换中的两个关键技术——滤波器的正则性与信号的边界处理

Two key technologies for image wavelet transform:The regularity of filters and the process of signal boundary

对图像小波变换中滤波器的正则性和信号的边界处理做了理论分析和仿真.小波滤波器的正则性关系到图像小波分解后信息量的分布以及图像恢复后失真量的大小.对一般较为平滑的图像而言,小波滤波器的正则性越高,其小波分解后信息量越集中,但对纹理较为复杂的图像来说,却并非如此.通过对信号的边界处理以及相位变化的分析和仿真,认为信号分解时向前、重构时向后的周期延拓是较好的方法,这样既可以保持信号的数据量不增加,又可以使恢复的信号相位不发生位移.

The regularity of wavelet filters on image wavelet transform for compression and coding is analyzed. The experimental results show that, for a flat image, the higher the regularity order is, the more concentrated is the information; but for a cross-grained image, this is not the case. In addition, the phase shift and boundary processing were also studied. The author considers that forward-period extension in decomposition and backward-period extension in reconstruction of signal are good strategy as it can keep the length and phase shift of the signal unchangeable.