基于偏微分方程的彩色图像乘性去噪模型

A Multiplicative Denoising Model of Color Images Based on Partial Differential Equations

提出一种新的非线性偏微分方程恢复模型,解决含乘性噪声的彩色图像恢复问题.新模型中引入光滑后向量值图像的几何流形特征判断图像的"真"、"假"边缘,利用p(x)-Laplace扩散系数在区域内部和边界以不同的方式进行扩散,利用u q扩散系数在乘性噪声干扰不同的区域以不同的速度进行扩散.理论分析和数值实验结果表明了该模型的有效性.

A nonlinear partial differential equation model was proposed to remove multiplicative noise of color images.The geometrical manifold characteristics of vector-valued image after smoothing are introduced to distinguish the ＂real＂ and ＂false＂ edges.The p（x）-Laplace diffusion coefficients drive image to diffuse in different ways on the edges and in the domains of images.The uq diffusion coefficient drives image to diffuse at different speeds that fit to the multiplicative noises strength.Theoretical analysis and numerical results show the efficiency of the new method.