中文摘要：

针对偏微分方程在图像处理中的斑点噪声滤除问题，在自适应全变分去噪模型和四阶LLT去噪模型的基础上，提出一种针对乘性噪声的自适应混合阶变分去噪方法。该方法引入混合阶偏微分方程和尺度自适应边缘检测函数作为正则项，并利用乘性噪声分布构建保真项。用标准测试数据对所提自适应混合阶变分降噪模型进行验证，试验结果表明，该模型在有效滤除图像乘性噪声的同时，能很好地保护图像的边缘和纹理细节信息。处理后的图像在峰值信噪比黼、均方误差MSE、运行效率方面均优于自适应全变分和LLT模型。

英文摘要：

An adaptive hybrid-order PDE method based on the adaptive total variation and a fourth-order PDE is proposed to reduce the multiplicative noise in images. A fidelity term constructed by noise distribution is used to enhance the edge of the image, when the adaptive hybrid-order partial differential equation is added as regular item. Denoising experiments on testing images show that the proposed method has higher capability of noise reduc- tion and image edge details preserving. The results show that the new method has better performance than the adap- tive total variation model and the LLT model in respects of PSNR： peak signal to noise ratio, MSE： mean square error and operating efficiency.