【摘要】 将边缘检测算子引入到用于图像去噪处理的四阶偏微分方程模型中,以建立能在去除图像中的噪声的同时抑制图像中的梯形效应且保护图像边缘细节的非线性偏微分方程模型.通过对该非线性偏微分方程模型的能量估计得到该非线性偏微分方程模型在有界区域上弱解的存在性和唯一性.利用数值仿真实验检验了所建立的非线性偏微分方程模型对图像中的高斯白噪声及椒盐噪声的去噪效果.更多还原

【Abstract】 An edge detection operator is introduced into a fourth-order partial differential equation model for denoising an image,which leads to a nonlinear partial differential equation model being capable of suppressing the ladder effect in the image and protecting the details of the edge of the image.The existence and uniqueness of the weak solution of the nonlinear partial differential equation in bounded areas is established by the energy estimation of the nonlinear partial differential equation.The denoising effect of the established nonlinear partial differential equation for the Gaussian white noise and the salt-and-pepper noise in the image is tested by numerical simulation experiments.更多还原