Abstract: The denoising model based on Partial Differential Equation (PDE) model cannot eliminate impulse noise and low-order PDE will produce blocky effect. In order to solve these problems, a denoising model combining PDE and adaptive median filtering was proposed. Through analyzing the image gradient, this model used second order model to denoise at the region with obvious gradient change and the region with tiny gradient change. At the smooth region, fourth order model was used to denoise. The region of the impulse noise was localized by making use of the characteristic that the gradient of the impulse noise is far bigger than the gradient of the edge. At this region, the adaptive median filtering was used to eliminate impulse noise. This method can eliminate impulse noise and protect the image edge effectively. It also can overcome the blocky effect and improve the denoising efficiency. The experiments prove the validity of the model.

Key words: image denoising, partial differential equation, adaptive median filtering, edge, impulse noise

摘要： 针对基于偏微分方程(PDE)的图像去噪模型不能有效地去除脉冲噪声，并且低阶偏微分方程在去噪的同时会出现“块效应”现象的问题，提出一种融合偏微分方程和自适应中值滤波的图像去噪模型。该模型通过对图像梯度的分析，在梯度变化剧烈区域和梯度变化微小区域利用二阶模型去噪以提高去噪效率；而在梯度渐变区域利用四阶模型平滑图像以避免出现“块效应”现象。同时，利用脉冲噪声梯度值远大于边缘梯度值的特点，定位脉冲噪声所在区域，在该区域利用自适应中值滤波消除脉冲噪声。该方法能有效去除脉冲噪声，保护图像边缘并消除“块效应”现象，同时提高了去噪效率。实验表明了该模型的有效性。

关键词: 图像去噪, 偏微分方程, 自适应中值滤波, 边缘, 脉冲噪声