基于Priwitt算子的偏微分方程图像去噪模型

PDE-based image noise removal models based on Priwitt operator

利用归一化的Priwitt微分算子作为权重,提出了两种融合Gauss曲率和平均曲率扩散的偏微分方程去噪模型,使得它们在去除噪声的同时能保持图像的重要特征。首先,对噪声图像进行Gauss滤波并计算滤波后图像的Priwitt微分算子;然后,新模型根据归一化的Priwitt微分算子自适应地平衡于高斯曲率扩散去噪与平均曲率扩散去噪之间,从而去除图像的噪声。利用偏微分方程有限差分法给出了新模型的离散迭代格式,并进行了数值实验。实验结果表明,新模型不仅迭代收敛的速度快,而且在均方误差和峰值信噪比两个评价指标上均优于单一曲率扩散去噪模型,并更好地保持了图像的细节特征。

Using the normal Priwitt operator as weights,two denoising models based on Partial Differential Equation（PDE）,which integrated the Gauss curvature and mean curvature diffusion,were proposed for keeping important features effectively while removing noises.First,the normal Priwitt operator of the filtered image obtained by the Gauss filter from noise image was calculated;second,the proposed models adaptively obtain the balance between the Gauss curvature diffusion noise removal and the mean curvature diffusion noise removal,thus removing noises of image.The iterative schemes of the proposed models were presented by the difference method of PDE.Then some numerical experiments were carried out.Results of experiments show that the proposed models not only converge quickly,but also are better than the denoising model based on single curvature diffusion,and better maintain the image features.