方向扩散方程与小波变换的相关性研究
doi: 10.3724/SP.J.1146.2006.01278
The Study of Correlation between Directed Diffusion Equation and Wavelet Transform
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摘要: 方向扩散方程是一种有方向性的扩散，本文基于这一特点，对方向扩散方程与小波分解和重构的相关性作了研究。首先，用小波分解后下层的低频图像作为对上层低频图像的一个初始近似，验证了由上层低频图像经方向扩散方程可逐渐扩散收敛到下层的低频图像；反过来，由下层低频图像经方向扩散方程亦可逐渐扩散恢复到上层低频图像，这正体现了小波分解与重构的渐变过程。因此，由方向扩散方程的迭代扩散可以实现小波变换在相邻两层间的分解与重构，且随着所选扩散时间间隔的减小，可以在越来越细的尺度上观察相邻两层间小波分解与重构的渐变过程。
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关键词:
- 方向扩散方程; 小波变换; 偏微分方程
Abstract: Based on the point that directed diffusion equation is a diffusion process with direction, the correlation between directed diffusion and wavelet transform is studied in this paper. At first, the last low-frequency image after wavelet decomposition can be an initial approximation of the next low-frequency image. It is tested and verified that the last low-frequency image can diffuse and converge to the next low-frequency image. On the other hand, the next low-frequency image can also diffuse and converge to the last low-frequency image. Above process just presents the gradual variation of wavelet decomposition and reconstruction. So the interative diffusion of directed diffusion equation can realize wavelet decomposition and reconstruction in two contiguous layers. With the reduction of time interval, the gradual variation of wavelet decomposition and reconstruction can be observed in more and more fine scales. -
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