The Study of Correlation between Directed Diffusion Equation and Wavelet Transform

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.