Abstract: The filter based on P-M diffusion equation directly has been proven to be efficient to the additive noise, but it often fails when facing the multiplicative noise（such as the SAR image speckle）. A novel speckle reduction method based on improved P-M diffusion equation is presented. By discussing the influence of applying log transfer to speckle, the theoretical foundation of applying P-M diffusion equation to speckle reduction is provided. A new diffusion coefficients based on Tukey’s Biweight Estimator error norm by recurring to the relationship between robust statistics and P-M diffusion is built. Simultaneously, the nonlinear time-dependent cooling technique for gradient threshold is incorporated into the new diffusion coefficients. In the experiment, the method is proven good performance in reducing speckle noise and preserving edges and details at the same time. Moreover, the filtered SAR images look good.

Key words: speckle, log-transform, Perona-Malik（P-M） diffusion equation, robust statistics, gradient threshold

摘要： 直接基于Perona-Malik扩散方程的滤波算法对于加性噪声非常有效，但是对于乘性噪声（如合成孔径雷达（SAR）图像相干斑噪声）收效甚微。提出了一种基于改进的Perona-Malik扩散方程抑制SAR图像相干斑噪声的新算法。分析对数变化对相干斑噪声的影响，为将P-M扩散方程应用于相干斑噪声抑制奠定了理论基础；通过P-M扩散和稳健统计学的联系，建立了基于Biweight Estimator误差模型的扩散系数；同时利用非线性衰减技术对梯度阈值的选择改进。实验表明，该方法不仅有效抑制了SAR图像相干斑噪声，较好地保持了细节和边缘信息，而且视觉效果比较好。

关键词: 相干斑, 对数变换, P-M扩散方程, 稳健统计, 梯度阈值