用小波矩阵分析Mallat算法的物理几何含义

The physical and geometry meaning of Mallat algorithm based on wavelet matrix analysi

提出了小波分析的新途径。用Harr小波矩阵来分析Mallat算法的物理和几何含义,把"原始像"分隔为"模糊像"和"细节像"。"模糊像"起到信息压缩的作用以利于远距离传输。本文同时给出如何把得到的"模糊像"经膨胀插值变成光滑的"恢复像",以体现滤波的效果。把"原始像"减去"恢复像"就得到按时间尺度分布的"总谐波像",以到达时频双分析效果。本文用Harr小波分解做到信息压缩和光滑重构,这些正是目前小波理论所梦寐以求的东西。

This paper presents new way of wavelet analysis, which indicates the physical and geometry meaning of Mallat algorithm by using of Harr wavelet matrix. The original image can be divided into blurred image and details image. And the blurred image serves as information compression in order to ease transmission. Also, this paper also discussed how the blurred image change into a smooth interpolation restore image to reflect the filtering effect. The original image subtracts the restore image to get a time-scale distribution of total harmonic image in order to get the time-frequency analysis. With Hart wavelet to decompose information then to achieve compression and smooth reconstruction result, these all is the stuff of dreams of the wavelet theory.