Abstract: Image denoising is an important branch in the field of digital image processing. The purpose is to remove the noise while maintaining the useful information such as contrast, clarity and texture of the image. It is the premise of image segmentation, feature extraction and target recognition and other image processing process. In order to effectively suppress the impulse noise and overcome the shortages of the harmonic model and the TV-[L1] model, a hybrid variational model with fidelity items for impulsive noise denoising is proposed. The numerical algorithm is realized by the augmented Lagrangian algorithm. The de-noising effect of the image is evaluated by peak signal-to-noise ratio, root mean square error. The experimental results show that the model has higher peak signal to noise ratio than other types of existing models, effectively reducing the root mean square error, and CPU time is shorter. This model has better denoising performance, a better visual effect is obtained. Not only the image quality is improved, but also the effectiveness is confirmed objectively.

摘要： 图像去噪技术是数字图像处理领域中一个重要的分支，目的是在去除噪声同时更好地保持图像的对比度、清晰度、纹理特征等有用的信息，它是图像分割、特征提取与目标识别等图像处理过程的前提。为了有效抑制脉冲噪声，针对调和模型和TV-[L1]模型去噪的不足，提出一种针对脉冲噪声去噪的带[L1]保真项的混合变分模型，并用增广拉格朗日算法进行数值实现。采用峰值信噪比、均方根误差指标评定图像的去噪效果。实验结果表明，该模型的峰值信噪比大于其他几类已有模型，有效降低了均方根误差，并且计算的CPU时间更短，去噪效果得到明显改善。该模型具有更好的去噪性能，获得了更理想的视觉效果，不仅能提高了图像质量，而且在客观上得到了有效证实。

关键词: 图像去噪, 变分法, 偏微分方程, 混合去噪模型, 数值仿真