小波变换点对称边界延拓问题研究

Research of point-symmetric boundary extension in wavelet transform

比较了几种小波变换的边界延拓方式,对小波变换的点对称延拓进行了边界点的光滑性分析,提出基于奇数长对称小波变换的点对称延拓方式,并证明了它在保持信号数据量不变的情况下是可以完全重构的。对一段有限信号分别采用对称延拓和点对称延拓进行小波分解重构计算,结果表明点对称延拓的重构精度比对称延拓的高。

This paper compared several boundary extensions based on wavelet transform. In particular, we analyzed the smoothness on boundary after point-symmetric extension, proposed a point-symmetric extension based on odd-length symmetric filter and proved that it preserved the perfect reconstruction while keeping the signal length unchanged. We used both symmetric extension and point-symmetric extension to analyze and reconstruct finite signals. The result shows that the point-symmetric extension＇s reconstruction precision is higher than the symmetric extension＇s.