基于偏微分方程的彩色图像乘性去噪模型

摘要

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 | u |q 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.