关键词: 相干斑, 对数变换, P-M扩散方程, 稳健统计, 梯度阈值

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