Abstract: From PM equation we derive muhi-dimensionay diffusion filtering equation discrete formula and its stable condition. We construct multi-scale decomposition and reconstruction method based on diffusion filtering, and provide two specific implementation plans. Application in practical seismic data shows that the method is reasonable and reliable. In the first plan 2D Fourier wave-number spectrum main energy is away from spectrum center with increase of scale, and residual signal acts at high wave numbers, which shows perfect application in random noise suppression. In the second plan 2D Fourier wave-number spectrum energy is close to spectrum center with increase of scale, and residual signal acts at low wave numbers, which shows perfect application in low-frequency reverse time migration noise suppression. The method computation is simple and easy to implement. It provides a multi-scale decomposition and reconstruction method for signal processing. It may has great application in seismic signal processing.

Key words: diffusion filtering, multi-scale decomposition, signal reconstruction, signal analysis, 2D wave-number spectrum