关键词: 微偏分方程, 多尺度分析, 图像去噪, 轮廓波变换, 核主成分分析, 图像扩散

Abstract: Aiming at the problem that the traditional image denoising algorithm had poor denoising effect and stability, we proposed an image denoising algorithm based on partial differential equation combined with multiscale analysis method. Firstly, the high frequency and low frequency bands of the image were processed by the second order partial differential diffusion equation and the fourth order partial differential equation, and the processed image was denoised as a whole by using the inverse transform of nondown sampling profile wave. Secondly, the contour wave transform method was used to decompose the whole image into different subbands,  the kernel principal component analysis algorithm was used to reduce the dimension of the whole image, and the different subbands were managed by blocks to complete the local denoising of the whole image. Finally, the image denoising based on partial differential equation and multiscale analysis method was realized. The experimental results show that the proposed algorithm has high image denoising effect and stability.

Key words: partial differential equation, multiscale analysis, image denoising, contour wave transform, kernel principal component analysis, image diffusion