Abstract:

In order to effectively suppress Gaussian-Poisson mixed noise, the edge region detail information and the Kullback-Leibler divergence can not be saved effectively for the harmonic model as a fidelity term（KL fidelity term）. The noise has the disadvantage of “step effect”. An image restoration variation model for Gaussian-Poisson mixed noise denoising is proposed. This model uses augmented Lagrangian algorithm for numerical implementation. Firstly, the harmonic model and the full variational model are fused according to the proportion, and the advantages of the two models are combined to enhance the denoising performance of the model. Then the Kullback-Leibler divergence is used as the guarantee. The true terms and fidelity terms are  mixed according to the proportion, which can effectively remove the Gauss-Poisson mixed noise and protect the edge details of the image. Finally, multiple images with different mixed noises are  used for comparison experiments. The peak signal-to-noise ratio and structural similarity index are used to evaluate the restoration effect of the image. Experimental results show that the peak signal-to-noise ratio and structural similarity of the model are larger than the Total Variation Kullback-Leible（TV-KL） model using the Kullback-Leibler divergence as a fidelity term, the improved MS model（Mix Regularization Term, MRT）, and Mix Fidelity Term（MFT）, and the calculated CPU time is shorter, and the denoising effect is significantly improved. This model has better denoising performance, effectively maintains the information of image details and texture features, and obtains more ideal visual effects. It not only improves the image quality, but also is effectively validated objectively. Ray image denoising has certain application value.

Key words: Gaussian-Poisson mixed noise, harmonic model, total variation Kullback-Leibler model, image restoration, variational method, partial differential equation, numerical simulation

摘要：

为了有效抑制高斯-泊松混合噪声，针对调和模型不能有效保存图像的边缘细节信息和Kullback-Leibler散度作为保真项（KL保真项）的全变差图像恢复模型对光滑的区域部分去噪会产生“阶梯效应”的不足，提出一种针对高斯-泊松混合噪声去噪的图像恢复变分模型。该模型利用增广拉格朗日算法进行数值实现，将调和模型和全变分模型按照比例进行融合，结合两种模型的优点，增强模型的去噪性能；Kullback-Leibler散度作为保真项和[L2]保真项按照比例进行混合，能有效去除高斯-泊松混合噪声的同时，保护图像的边缘细节；使用多幅含不同混合噪声的图像进行对比实验，采用峰值信噪比、结构相似度指标评定图像的恢复效果。实验结果表明，该模型的峰值信噪比和结构相似度大于使用Kullback-Leibler散度作为保真项的全变差图像恢复（TV-KL）模型、改进MS模型（MRT），以及保真项混合模型（MFT）这三个模型，并且计算的CPU时间更短，去噪效果得到明显改善。所提模型具有更好的去噪性能，有效地保持了图像细节和纹理特征方面的信息，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的证实，可以应用于X射线图像去噪。

关键词: 高斯-泊松混合噪声, 调和模型, 全变差图像恢复模型, 图像恢复, 变分法, 偏微分方程, 数值仿真